q115/random_k4/random_3.md

CounterBench: Evaluating and Improving Counterfactual Reasoning in
|     |                    | Large         | Language                      | Models  |     |                |       |     |     |     |
| --- | ------------------ | ------------- | ----------------------------- | ------- | --- | -------------- | ----- | --- | --- | --- |
|     | YuefeiChen1        | VivekK.Singh1 |                               | JingMa2 |     | RuixiangTang1* |       |     |     |     |
|     | 1RutgersUniversity |               | 2CaseWesternReserveUniversity |         |     |                |       |     |     |     |
|     | Abstract           |               |                               |         |     |                | Back. |     |     |     |
6202 rpA 11  ]LC.sc[  2v80011.2052:viXra Counterfactualreasoningiswidelyrecognized 74.5
|                                             |                      |               |     |     | Basic |               | 58.5  |          | Nested |     |
| ------------------------------------------- | -------------------- | ------------- | --- | --- | ----- | ------------- | ----- | -------- | ------ | --- |
| as one of                                   | the most challenging | and intricate |     |     |       |               |       |          |        |     |
|                                             |                      |               |     |     |       | 98.4 75.272.4 | 53. 0 | 76.078.4 | 94.0   |     |
| aspectsofcausalityinartificialintelligence. |                      |               | In  |     |       |               |       |          |        |     |
54.8 5 0.8
thispaper,weevaluatetheperformanceoflarge
5 8 .8
65 . 6 50.8
| languagemodels(LLMs)incounterfactualrea- |     |     |     |     |     |     |      | 67.2 |     |     |
| ---------------------------------------- | --- | --- | --- | --- | --- | --- | ---- | ---- | --- | --- |
|                                          |     |     |     |     |     |     | 70.8 | 72.4 |     |     |
soning. Incontrasttopreviousstudiesthatpri-
|                                       |     |     |     |     |     | 89.6  |     | 90.0  |     |     |
| ------------------------------------- | --- | --- | --- | --- | --- | ----- | --- | ----- | --- | --- |
| marilyfocusoncommonsensecausalreason- |     |     |     |     |     | Cond. |     | Joint |     |     |
ing,whereLLMsoftenrelyonpriorknowledge
|     |     |     |     |     |     | Our CoIn |     | Standard |     |     |
| --- | --- | --- | --- | --- | --- | -------- | --- | -------- | --- | --- |
forinference,wespecificallyassesstheirabil-
|     |     |     |     |     |     | CausalCoT |     | Solver |     |     |
| --- | --- | --- | --- | --- | --- | --------- | --- | ------ | --- | --- |
itytoperformcounterfactualinferenceusinga
| setofformalrules. | Tosupportthisevaluation, |     |     |     |     |     |     |     |     |     |
| ----------------- | ------------------------ | --- | --- | --- | --- | --- | --- | --- | --- | --- |
Figure1: ComparisonofaccuracyscoresontheCoun-
weintroduceanewbenchmarkdataset,Coun- terBench dataset across different strategies: our pro-
terBench,comprising1.2Kcounterfactualrea-
posedCoInparadigmversusbaselineapproaches(Stan-
| soningquestions. | Thedatasetisdesignedwith |     |     |       |           |      |         |        |            |      |
| ---------------- | ------------------------ | --- | --- | ----- | --------- | ---- | ------- | ------ | ---------- | ---- |
|                  |                          |     |     | dard, | CausalCoT | (Jin | et al., | 2023), | and Solver | (Hua |
varyinglevelsofdifficulty,diversecausalgraph et al., 2024)), evaluated using Gemini-1.5-flash. Our
structures,distincttypesofcounterfactualques-
|     |     |     |     | CounterBenchdatasetincludesfivekindstypes. |     |     |     |     |     | Basic |
| --- | --- | --- | --- | ------------------------------------------ | --- | --- | --- | --- | --- | ----- |
tions,andmultiplenonsensicalnamevariants. focusesonexploringhowasinglechangeinacausal
Ourexperimentsdemonstratethatcounterfac-
variable. Jointinvolvessimultaneouschangesinmul-
tualreasoningposesasignificantchallengefor
tiplecauses,Nestedinvolvesstepwisehypotheticalas-
LLMs,withmostmodelsperformingatlevels sumptionsaboutmultiplevariables. Conditionaleval-
| comparabletorandomguessing. |     | Toenhance |     |                                              |     |     |     |     |     |     |
| --------------------------- | --- | --------- | --- | -------------------------------------------- | --- | --- | --- | --- | --- | --- |
|                             |     |           |     | uatescounterfactualsunderobservedconditions. |     |     |     |     |     | And |
LLM’scounterfactualreasoningability,wepro- Backdoorinvolvescounterfactualreasoninginthepres-
poseanovelreasoningparadigm,CoIn,which enceofbackdoorpathsthatcreateconfoundingbetween
guidesLLMsthroughiterativereasoningand
thetreatmentvariableandtheoutcome.
backtrackingtosystematicallyexplorecounter-
| factual solutions. | Experimental         | results  | show |        |         |       |     |         |       |         |
| ------------------ | -------------------- | -------- | ---- | ------ | ------- | ----- | --- | ------- | ----- | ------- |
| that our           | method significantly | improves | LLM  |        |         |       |     |         |       |         |
|                    |                      |          |      | Koonce | et al., | 2011; | Gow | et al., | 2016; | Loi and |
performanceoncounterfactualreasoningtasks
|     |     |     |     | Rodrigues,2012). |     |     | Forexample,aconsumerwho |     |     |     |
| --- | --- | --- | --- | ---------------- | --- | --- | ----------------------- | --- | --- | --- |
andconsistentlyenhancesperformanceacross
declinedanextendedwarrantymaylaterwonder,
| different | LLMs. Our dataset | is available | at  |     |     |     |     |     |     |     |
| --------- | ----------------- | ------------ | --- | --- | --- | --- | --- | --- | --- | --- |
“WhatifIhadpurchasedit,couldIhaveavoidedthe
https://huggingface.co/datasets/CounterBench
/CounterBench. repaircosts?” Thisillustrateshowcounterfactual
|                |     |     |     | reasoning                                     | guides | decision-making |     |        | by    | evaluating |
| -------------- | --- | --- | --- | --------------------------------------------- | ------ | --------------- | --- | ------ | ----- | ---------- |
| 1 Introduction |     |     |     | missedopportunitiesandalternativeoutcomes(Kr- |        |                 |     |        |       |            |
|                |     |     |     | ishnamurthy                                   |        | and Sivaraman,  |     | 2002). | While | tradi-     |
Counterfactualreasoning,residingatthepinnacle
tionalcausalinferencemethods(SharmaandKici-
ofPearl’sCausalHierarchy(PearlandMackenzie,
|     |     |     |     | man, | 2020; | Chen et | al., 2020; | Feder | et  | al., 2022) |
| --- | --- | --- | --- | ---- | ----- | ------- | ---------- | ----- | --- | ---------- |
2018),underpinsthe“whatif”inquiriesessentialto
haveenhancedthepredictiveaccuracy,robustness,
humancognitionanddecision-makingacrosscrit-
andexplainabilityofNLPmodels,recentprogress
icalfieldssuchashealthcare,business,publicad-
inLLMshasfurtherenrichedourabilitytocapture
ministration,andscience(Gvozdenovic´etal.,2021;
|     |     |     |     | nuanced | causal | dependencies |     | (Liu | et  | al., 2024a; |
| --- | --- | --- | --- | ------- | ------ | ------------ | --- | ---- | --- | ----------- |
Kyrimietal.,2025;KasirzadehandSmart,2021;
Petronietal.,2019;Liangetal.,2024;Tarassow,
*CorrespondingEmail:ruixiang.tang@rutgers.edu 2023;Ma,2024;Liuetal.,2024b). Theseadvance-

mentsnotonlydemonstratesophisticatedreasoning cess,guidingLLMsthroughabduction,action,it-
intasksrangingfromwritingtoprogrammingbut erativeprediction,andbacktrackingvalidationto
also pave the way toward emulating human-like systematically formalize and explore counterfac-
intelligenceandachievingartificialgeneralintelli- tual paths. This structured mechanism dynami-
gence(LiandLi,2024;Alwin,2023;Sahota,2023; callyassessesthepromiseofeachinferencestep,
Bubecketal.,2023). enabling reversion to more promising points and
Despiterecentadvancements,progressincoun- ensuringlogicalconsistency,particularlyinlong-
terfactual reasoning using LLMs remains con- chain causal dependencies. This systematic pro-
strained by two primary challenges. First, there cesssubstantiallyimprovestheaccuracyofcoun-
is currently no dedicated benchmark dataset for terfactualanalysis. ExperimentsonCounterBench
rigorouslyevaluatingLLMs’performanceoncoun- demonstrate that CoIn achieves an accuracy of
terfactualtasks,makingitdifficulttomeasurethe 89.9%,deliveringanearly20%improvementover
models’ capacity to capture nuanced causal rela- Gemini-1.5-flashcomparedtoalternativestrategies
tionships. Second,evenwithadvancedprompting (seeFigure1). Theframeworkofthisworkisillus-
techniques,CausalCoT(Jinetal.,2023)andother tratedinFigure2. Thecontributionsofthiswork
iterativemethods,LLMsoftenstruggletoproduce aresummarizedasfollows:
logicallyconsistent,contextuallyappropriatecoun-
terfactuals (Ma, 2024; Jin et al., 2023; Kıcıman • Webuildacomprehensivedataset,Counter-
etal.,2023;Zecˇevic´ etal.,2023). Inresponse,this Bench. Thedatasetcontainsover1200long-
paperfocusesontwokeyquestions: chaincomplexcounterfactualreasoningques-
HowwelldoLLMshandlecounterfactualrea- tions. The dataset spans multiple difficulty
soning? Theabsenceofastandardizedbenchmark levels,diversecausalgraphstructures,various
datasethasimpededrigorousempiricalevaluation typesofcounterfactualquestions,andawide
ofLLMs’capabilitiesincapturingintricatecausal range of nonsensical variant name combina-
relationships within complex counterfactual rea- tions.
soningtasks. Toaddressthis,wepresentCounter-
Bench,acomprehensiveevaluationframeworkde- • WebenchmarkLLMswithvariousinference
signedtoassesscounterfactualreasoningthrough strategies on CounterBench, and results re-
1.2Kquestionsencompassingvariousdomainsand vealthatmostexistingmodels(e.g.,GPT-4o
reasoningtypes. Bysystematicallyevaluatingfive andDeepseek-V3)exhibitlimitedcapabilities
keydimensions,itdemandsgenuinereasoningbe- inperformingcounterfactualinferencetasks.
yondpatternrecognitionormemorizedresponses.
Ourexperimentsexposenotableperformancelim- • WeproposeanovelreasoningparadigmCoIn
itations in LLMs, even those equipped with ad- guides LLMs through abduction, action, it-
vanced inference techniques. Most models like erative prediction, and backtracking valida-
GPT-4oandDeepseek-V3achieveaccuracyofap- tiontosystematicallyformalizeandexplore
proximately50%,equivalenttorandomguessing. counterfactual reasoning paths. It achieves
Furthermore,ourevaluationofstate-of-the-artin- nearly90%accuracyonseveralstate-of-the-
ference strategies shows only marginal improve- artLLMsevaluatedonCounterBench,repre-
mentsoverbaselineperformanceformostmodels. sentinga20%improvementovertheprevious
Themodelsconsistentlystrugglewithmaintaining bestbaseline.
logicalcoherenceduringmulti-stepreasoningpro-
cessesandaccuratelyhandlingcausalrelationships
incomplexscenarios. 2 CounterBench
How to improve LLMs’ counterfactual rea-
soningabilities? Toadvancelargelanguagemod- Toevaluatethecounterfactualreasoningcapabili-
els’counterfactualreasoningcapabilities,thispa- tiesofLLMs,weintroduceacomprehensivebench-
per presents CoIn (Counterfactual Inference), a markingdatasetspecificallydesignedtomeasure
novel approach that explicitly tackles the critical their ability to handle complex causal reasoning
challengesofmulti-stepinference,whichremain tasks. This section details the structure of the
unresolvedbypreviousmethods. CoInembedsa dataset,themethodologyforquerygeneration,and
tailored search algorithm into the reasoning pro- thebenchmarkingresultsanalysis.

CounterBench Dataset       Benchmarking LLMs      CoIn Reasoning Strategy
|     | Basic |     |     | Standard Strategy |     |     |     | Extraction |     |
| --- | ----- | --- | --- | ----------------- | --- | --- | --- | ---------- | --- |
without Instruction
Joint
Abduction and Intervention Action
|     | Nested | Human        |     |                 | Error    |     |     |     |     |
| --- | ------ | ------------ | --- | --------------- | -------- | --- | --- | --- | --- |
|     |        | Verification |     | Solver Strategy | Analysis |     |     |     |     |
Forward Inference
Conditonal
|     | Backdoor |     |     | CausalCoT Strategy |     |     | Back-tracking Validation |     |     |
| --- | -------- | --- | --- | ------------------ | --- | --- | ------------------------ | --- | --- |
Figure2: Illustrationoftheframework. WecreateCounterBench,adatasetfeaturingfivetypesofcounterfactual
questions(basic,joint,conditional,nested,andbackdoor). Basedonthisdataset,webenchmarkstate-of-the-art
LLMsusingvariousinferencestrategies,conductcomprehensiveerroranalysis,andproposeourCoInreasoning
frameworkfeaturingsystematicinferencewithvalidationmechanisms.
| Type | QueryTemplateExample |     |     |     |     |     | Causalgraph |     |     |
| ---- | -------------------- | --- | --- | --- | --- | --- | ----------- | --- | --- |
WeknowthatXcausesV1,V1causesV2,V2causesV3,andV3causesV4,
Basic
V4causesV5,V5causesY.WouldYoccurifnotXinsteadofX?
WeknowthatXcausesV1,V1causesV2,V2andV1togethercauseV3,
| Joint | V3causesV4,V4andXtogethercauseV5,andV5causesY. |     |     |     |     |     |     |     |     |
| ----- | ---------------------------------------------- | --- | --- | --- | --- | --- | --- | --- | --- |
WouldYoccurifnotXandnotV3?
WeknowthatXcausesV1,V1causesV2,V2andV1togethercauseV3,
V3causesV4,V4andV2togethercauseV5,andV5causesY.
Nested
AssumenotX,andbasedonthisassumption,furthersupposenotV4.
WouldYoccur?
WeknowthatXandV1togethercauseV2,V2causesV3,V3causesV4,
| Conditional | V4causesV5,V5causesY.WeobservedV1.WouldYoccurifnotX |     |     |     |     |     |     |     |     |
| ----------- | --------------------------------------------------- | --- | --- | --- | --- | --- | --- | --- | --- |
insteadofX?
X
WeknowthatV1causesX,XandV1togethercauseV2,V2causesV3,
| Backdoor |     |     |     |     |     |     |     | V2 V3 | V4 V5 Y |
| -------- | --- | --- | --- | --- | --- | --- | --- | ----- | ------- |
V3andXtogethercauseV4,V4causesV5,andV5causesY.
V1
|     |     |     | Table1: | IllustrativeCounterfactualQueryTypes |     |     |     |     |     |
| --- | --- | --- | ------- | ------------------------------------ | --- | --- | --- | --- | --- |
2.1 DatasetStructure BasicCounterfactual. Thebasiccounterfactual
|     |     |     |     |     | typeaddressessimple“what-if”scenarios. |     |     |                   | Inthis |
| --- | --- | --- | --- | --- | -------------------------------------- | --- | --- | ----------------- | ------ |
|     |     |     |     |     | scenario,itisformalizedasY             |     |     | (u),whichservesas |        |
x
The dataset consists of two main components: a apotentialoutcomeexpression. Incausalreason-
|        |                |         |     |               | ing, potential | outcomes | refer | to the | hypothetical |
| ------ | -------------- | ------- | --- | ------------- | -------------- | -------- | ----- | ------ | ------------ |
| set of | counterfactual | queries | and | corresponding |                |          |       |        |              |
binary answers. Formally, the dataset is defined resultsobservedwhenavariableissettoapartic-
as D := {(q ,a )|i = 1,2,...,N}, where each ular value (Holland, 1986). In Y (u) expression,
|     | i i |     |     |     |     |     |            | x   |     |
| --- | --- | --- | --- | --- | --- | --- | ---------- | --- | --- |
|     |     |     |     |     | Y   |     | variable,x |     |     |
q is a counterfactual query, and a ∈ {yes,no} is the outcome is the value consid-
| i          |             |         |      | i            |         |                  |     |           |               |
| ---------- | ----------- | ------- | ---- | ------------ | ------- | ---------------- | --- | --------- | ------------- |
|            |             |         |      |              | ered in | the hypothetical |     | scenario, | and u denotes |
| represents | the correct | answer. | Each | query is de- |         |                  |     |           |               |
rivedfromadeterministicStructuralCausalModel the context. To illustrate, consider a lawn irriga-
(SCM)M = ⟨U,V,f⟩,whereU isthesetofexoge- tionsystemthatonlyactivateswhentheweatheris
|                                 |     |     |     |            | sunny and | the soil | is dry. | In this example, | Y (u) |
| ------------------------------- | --- | --- | --- | ---------- | --------- | -------- | ------- | ---------------- | ----- |
| nousvariableswithassignmentsu,V |     |     |     | isthesetof |           |          |         |                  | x     |
endogenousvariables,andf isthesetofstructural describesthesystem’spotentialbehaviorwhenthe
equations(Pearl,2009). ForeachV ∈ V,wehave weatherconditionxisimposedwhilethesoilcondi-
i
|     |             |             |     |               | tion(contextu)remainsunchanged. |     |     |     | Consequently, |
| --- | ----------- | ----------- | --- | ------------- | ------------------------------- | --- | --- | --- | ------------- |
| V = | f (Pa(V ),U | ),wherePa(V |     | ) ⊆ V denotes |                                 |     |     |     |               |
| i   | i i         | i           | i   |               |                                 |     |     |     |               |
whenaskingwhetherthesystemwouldactivateif
| the parents | of V i , | and U i refers | to  | the subset of |     |     |     |     |     |
| ----------- | -------- | -------------- | --- | ------------- | --- | --- | --- | --- | --- |
exogenousvariablesfromU thatdirectlyinfluence theweatherchangedtocloudy,therelevantcoun-
the value of V . Intervening on a set of variables terfactualoutcomeisY cloudy (u).
i
X ⊆ V andsettingthemtoxmodifiesthemodelto
M ,whichdeterministicallydefinesthevaluesof JointCounterfactual. Thistypeinvolvesacoun-
x
intervenedvariablesgivenu. Thedatasetincludes terfactualscenarioinwhichmultiplevariablesare
fivetypesofcounterfactualqueries: set simultaneously. Formally, it is expressed as

|     |     |     | Standard |     |     |     | CausalCoT |     |     |
| --- | --- | --- | -------- | --- | --- | --- | --------- | --- | --- |
Models Basic Cond. Joint NestedBack. Avg. Basic Cond. Joint NestedBack. Avg.
GPT-3(Davinci-002) 56.8 50.2 48.8 51.6 52.5 51.9 51.2 41.9 51.2 51.6 50.5 49.3
GPT-3(Babbage-002) 50.0† 50.0† 50.0† 50.0† 47.5 49.6 3.6* 7.6* 1.2* 19.6* 18.5* 9.8*
GPT-3.5 49.6 51.2 50.4 50.0 52.0 50.6 43.6 50.4 53.6 50.0 47.5 49.1
GPT-4omini 50.0† 50.0† 50.0† 50.0† 52.5 50.4 57.2 66.4 60.0 63.2 50.0 59.8
GPT-4o 50.4 54.4 50.4 54.8 54.0 52.8 80.4 72.4 80.8 81.6 60.5 75.8
Claude-3(Sonnet) 50.4 48.8 50.0 50.8 59.5 51.6 59.2 52.0 64.4 60.0 65.5 59.0
Claude-3.5(Haiku) 28.4 24.0 43.6 54.0 51.0 39.8 60.4 65.6 67.2 66.0 61.0 64.2
Gemini-1.5-flash 75.2 65.6 67.2 76.0 53.0 68.0 72.4 70.8 72.4 78.4 58.5 71.0
Gemini-1.5-flash-8b 50.0† 50.0† 50.0† 50.0† 52.5 50.4 66.8 67.2 65.2 65.2 58.5 64.8
Deepseek-V3 50.4 50.4 50.0 50.0 60.5 51.9 80.8 70.4 76.4 77.6 63.5 74.2
Table2: ModelaccuracyofstandardmethodandCausalCoTacrossdifferentreasoningcategories. Note: *The
averageaccuracyisonly9.8%becausemostofresponsesarenot“Yes”or“No”but“incomprehensible”,which
meansLLMcannotfollowinstructionofCausalCoTinstructionwelltoinfer. Moredetailswillbeexplainedinthe
AppendixH.†indicatesthattheLLMpredictsallquestionsaseither“Yes”or“No”,leadingtoa50%accuracy.
Y x,z (u),representingtheoutcomeY aftersetting observedassunny,thequeryevaluateswhetherthe
X = xandZ = z. Forinstance,alawnirrigation lawn irrigation system still activate or not if the
systemwillactivateiftheweatherissunny,butit sensordetectsmoistsoilinsteadofdryness. Here,
alsorequiresdrysoilasatrigger. SupposeZ repre- Z = z representstheweatherisobservedassunny,
sentstheweatherconditionandX representsthe whichisagivenconditionforreasoning.
| soilmoisturecondition. |     | Thequeryasksiftheirriga- |     |     |     |     |     |     |     |
| ---------------------- | --- | ------------------------ | --- | --- | --- | --- | --- | --- | --- |
tionsystemwillactivatewhentheweatherchanges
| to cloudy and   | the sensor                    | detects | that the soil is |     |     |     |     |     |     |
| --------------- | ----------------------------- | ------- | ---------------- | --- | --- | --- | --- | --- | --- |
| moistmeanwhile. | Therelevantcounterfactualout- |         |                  |     |     |     |     |     |     |
comeisY (u). Thisscenarioexamines Backdoor Counterfactual. This type involves
cloudy,moist
thecombinedeffectofbothactionshappeningsi- counterfactual reasoning in the presence of back-
|     |     |     |     | door paths | that create | confounding |     | between | the |
| --- | --- | --- | --- | ---------- | ----------- | ----------- | --- | ------- | --- |
multaneously.
treatmentvariableandtheoutcome(Pearl,2009).
NestedCounterfactual. Nestedcounterfactual Formally, it addresses queries of the form Y x (u)
|                     |              |     |               | when there | exist | backdoor | paths | from X | to Y |
| ------------------- | ------------ | --- | ------------- | ---------- | ----- | -------- | ----- | ------ | ---- |
| involves sequential | dependencies |     | between vari- |            |       |          |       |        |      |
ables. This is represented as Y (u), where an throughconfounders. Insuchscenarios,thecausal
Zx
interventiononX affectsZ,whichinturnimpacts effect cannot be directly identified without con-
|                 |        |         |                  | trolling | for the confounding |     | variables | along | the |
| --------------- | ------ | ------- | ---------------- | -------- | ------------------- | --- | --------- | ----- | --- |
| Y. For example, | if the | weather | had been cloudy, |          |                     |     |           |       |     |
whichisacounterfactualweatherstate,andunder backdoor paths. For example, a manager consid-
thisscenario,thesensordetectedmoistsoilinstead ersevaluatingwhetheranewmarketingcampaign
of dry soil, would the irrigation system activate? would increase sales if it is implemented. How-
Inthisframework,Z representstheweathercondi- ever,boththedecisiontolaunchthecampaignand
tion,X isthesoilmoisturereading. Z dependson thesalesoutcomemightbeinfluencedbyseasonal
thecounterfactualvalueofX throughthesystem’s demand patterns. Here, the backdoor path runs
|     |     |     |     | from the | marketing | campaign | through | seasonal |     |
| --- | --- | --- | --- | -------- | --------- | -------- | ------- | -------- | --- |
structuralcausalrelationships.
|     |     |     |     | demand | to sales, | creating | a spurious | association. |     |
| --- | --- | --- | --- | ------ | --------- | -------- | ---------- | ------------ | --- |
Conditional Counterfactual. This type intro- The counterfactual query “Would sales increase
ducesobservedconditionsintothecounterfactual if we launched the campaign?” requires account-
world (Pearl, 2009). Formally, it is written as ingforthisconfoundingbyeithercontrollingfor
Y (u) | Z (u) = z, askinghowY wouldchange seasonaleffectsorusingotheridentificationstrate-
| x x |     |     |     |     |     |     |     |     |     |
| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |
ifX wassettoxwhileZ = z beingobservedas gies. Inourdataset,backdoorcounterfactualstest
a condition. For example, a lawn irrigation sys- whether LLMs can distinguish between genuine
temwillactivateiftheweatherissunny,butitalso causaleffectsandspuriouscorrelationswhenrea-
requiresdrysoilasatrigger. Nowtheweatheris soningaboutalternativescenarios.

2.2 QueryGenerationandQuality 2022). Byintegratingasystematicderivationpro-
| Assessment |          |     |            |             |     | cess,includingcausalgraphextraction,querytype |     |                  |     |     |                |     |
| ---------- | -------- | --- | ---------- | ----------- | --- | --------------------------------------------- | --- | ---------------- | --- | --- | -------------- | --- |
|            |          |     |            |             |     | classification,                               |     | data collection, |     | and | formalization, |     |
| Each query | consists | of  | background | information |     |                                               |     |                  |     |     |                |     |
CausalCoTensuresrobustlogicalconsistencyand
| and a specific | question. |     | Table | 1 illustrates | how |     |     |     |     |     |     |     |
| -------------- | --------- | --- | ----- | ------------- | --- | --- | --- | --- | --- | --- | --- | --- |
highreasoningaccuracy.
samplesaregeneratedusingvariousdeterministic
|                           |             |        |                     |                  |     | EvaluationSettings. |     |                | Withinourevaluationframe- |      |       |          |
| ------------------------- | ----------- | ------ | ------------------- | ---------------- | --- | ------------------- | --- | -------------- | ------------------------- | ---- | ----- | -------- |
| counterfactualquerytypes. |             |        | Thebackgroundiscon- |                  |     |                     |     |                |                           |      |       |          |
|                           |             |        |                     |                  |     | work, responses     |     | are classified |                           | into | three | distinct |
| structed                  | with causal | graphs | and                 | story templates, |     |                     |     |                |                           |      |       |          |
categories,“Yes”,“No”,and“Incomprehensible”.
andvariablenamesarereplacedbynonsensical,ar-
Thelatterencompassingresponsesthatareeither
tificiallygeneratedwords(e.g.,“Kelp,”“Ziklo”)to
ambiguousorlackclearmeaning,typicallymani-
preventmodelsfromrelyingonmemorizedknowl-
festingwhennoanswerisdetected,suchasNULL
| edge. In | this way, | we  | force LLMs | to engage | in  |         |         |       |         |        |            |     |
| -------- | --------- | --- | ---------- | --------- | --- | ------- | ------- | ----- | ------- | ------ | ---------- | --- |
|          |           |     |            |           |     | returns | or mere | query | echoes. | During | inference, |     |
causalreasoningratherthanusingpriorknowledge
|                |       |     |         |               |      | wesetthetemperatureat0. |     |     |     | Weemployinference |     |     |
| -------------- | ----- | --- | ------- | ------------- | ---- | ----------------------- | --- | --- | --- | ----------------- | --- | --- |
| in pretraining | data. | The | dataset | also features | bal- |                         |     |     |     |                   |     |     |
accuracyasourprimaryperformancemetric.
| anced distributions |     | in multiple |     | dimensions, | with |     |     |     |     |     |     |     |
| ------------------- | --- | ----------- | --- | ----------- | ---- | --- | --- | --- | --- | --- | --- | --- |
binaryresponsesevenlysplitbetween50%“Yes” 3.1 ExperimentalResults
and50%“No.”Thisbalanceextendsacrossdiffer-
AsshowninTable2,theresultsindicatethatwith-
entquestiontypesanddifficultylevels,ensuringa
outspecificinstructions,mostLLMsstrugglewith
uniformresponsedistributionwithineachcategory.
counterfactualreasoning,performingnobetterthan
Thedatasetconsistsof1,200questions,categorized
|     |     |     |     |     |     | randomguessingintermsofaccuracy. |     |     |     |     | Specifically, |     |
| --- | --- | --- | --- | --- | --- | -------------------------------- | --- | --- | --- | --- | ------------- | --- |
intofivedistincttypes,witheachtypecontaining
|                    |     |                          |     |     |     | for model   | GPT-4o | mini,  | we    | observed | consistent |     |
| ------------------ | --- | ------------------------ | --- | --- | --- | ----------- | ------ | ------ | ----- | -------- | ---------- | --- |
| 200or250questions. |     | Withineachtype,thereisan |     |     |     |             |        |        |       |          |            |     |
|                    |     |                          |     |     |     | predictions | of     | either | “Yes” | or “No,” | resulting  | in  |
equaldistributionofanswers,comprising100“Yes”
|           |         |               |           |         |            | a 50.0%                                      | accuracy | in  | the first | four | kinds | of ques- |
| --------- | ------- | ------------- | --------- | ------- | ---------- | -------------------------------------------- | -------- | --- | --------- | ---- | ----- | -------- |
| responses | and 100 | “No”          | responses | or 125  | “Yes”      |                                              |          |     |           |      |       |          |
|           |         |               |           |         |            | tions. Amongalltestedmodels,Gemini-1.5-flash |          |     |           |      |       |          |
| and 125   | “No”.   | Additionally, | the       | dataset | is strati- |                                              |          |     |           |      |       |          |
achievedthehighestbaselineperformancewithan
| fied based | on five | levels | of difficulty, | determined |     |          |           |          |     |     |           |     |
| ---------- | ------- | ------ | -------------- | ---------- | --- | -------- | --------- | -------- | --- | --- | --------- | --- |
|            |         |        |                |            |     | accuracy | of 68.0%. | Although |     | the | CausalCoT | ap- |
bythenumberofeventspresentineachquestion,
proachisdesignedtoenhancethecausalreasoning
| rangingfrom5to9. |     | Eachdifficultylevelincludes |     |     |     |     |     |     |     |     |     |     |
| ---------------- | --- | --------------------------- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |
capabilitiesofLLMs,ourempiricalfindingssug-
240questions,maintainingabalanceddistribution
gestthatitdoesnotsignificantlyimprovetheirper-
| ofanswerswith120“Yes”and120“No”. |     |     |     |     | Wealso |                                         |     |     |     |     |     |      |
| -------------------------------- | --- | --- | --- | --- | ------ | --------------------------------------- | --- | --- | --- | --- | --- | ---- |
|                                  |     |     |     |     |        | formanceincounterfactualreasoningtasks. |     |     |     |     |     | Most |
conductahumanevaluationonthesequeries,with
modelsshowedminimalornoimprovement,asex-
furtherdetailsprovidedinAppendixB.
|     |     |     |     |     |     | emplifiedbyGPT-3.5Turbo. |               |     |     | Thebestperformance |          |     |
| --- | --- | --- | --- | --- | --- | ------------------------ | ------------- | --- | --- | ------------------ | -------- | --- |
|     |     |     |     |     |     | model in                 | the CausalCoT |     | is  | GPT-4o,            | achieved | an  |
3 BenchmarkingLLMsonCounterBench
accuracyofonly75.8%.
Weconductedcomprehensiveexperimentstosys- ErrorAnalysis. Tosystematicallyanalyzethelim-
tematically evaluate the performance of current itations of existing approaches, we conducted an
LLMs on counterfactual reasoning tasks, demon- error analysis on responses generated by Causal-
stratingtheircapabilitiesusingstate-of-the-artrea- CoT. Our analysis focuses on three key compo-
soningtechniques.
|     |     |     |     |     |     | nents: causal |     | data collection, |     | inference |     | process, |
| --- | --- | --- | --- | --- | --- | ------------- | --- | ---------------- | --- | --------- | --- | -------- |
Models. The tested LLM models include GPT- and conclusion derivation. Through careful ex-
3.5 turbo, GPT-4o, GPT-4o mini, Davinci-002, aminationofeachcomponent,weidentifiedthree
Babbage-002(OpenAI,2024),Claude3.5Haiku, primarycategoriesoferrors: Wrongcausalrela-
Claude 3 Sonnet (Anthropic, 2024), Deepseek- tionships: This error occurs when LLMs cannot
V3 (DeepSeek, 2024) and Gemini-1.5-Flash and constructaccuratecausalgraphsorextractknown
Gemini-1.5-Flash-8B(Google,2024). valuesfrombackgroundinformation. Wronginfer-
ReasoningStrategies. Inourbaselineevaluations, enceprocess: ThishappenswhenLLMs,despite
we employed two distinct reasoning strategies to correctlyidentifyingcausalrelationships,makein-
assess these models. The first relied on standard correctpredictionsofthetargeteventY. Wrong
prompting methods without specialized instruc- conclusion: ThistypeoferrorariseswhenLLMs
tions. The second used the advanced CausalCoT reach contradictory final answers, even after cor-
approach (Jin et al., 2023), an extension of the rectlycomputingthevalueofY. Thedistribution
Chain-of-Thoughtpromptingparadigm(Weietal., of these error categories is illustrated in Figure

3. Notably, 86% of errors occur in the inference Each phase serves a specific purpose in ensuring
process,revealingthatevenwithwell-constructed accurate counterfactual reasoning, and they pro-
causal graphs, LLMs struggle significantly with vide a robust methodology for handling complex
derivingaccuratepredictionsthroughreasoning. causaldependenciestogether. Below,wedescribe
eachphaseindetail,explainingitsroleandhowit
contributestotheoverallprocess.
4.1 Extraction
Inthefirstphase,wefocusonsystematicallygath-
12%
|     | 2%  |     | ering all      | relevant information |                | explicitly | stated           | in    |
| --- | --- | --- | -------------- | -------------------- | -------------- | ---------- | ---------------- | ----- |
|     |     |     | the scenario.  | The                  | process        | begins     | with construct-  |       |
|     |     |     | ing the causal | graph                | by identifying |            | relationships    |       |
|     |     |     | between        | events and           | representing   |            | them in a        | clear |
|     |     |     | “event 1       | → event              | 2” format,     |            | which eliminates |       |
|     |     | 86% | potential      | ambiguities.         | Next,          | we         | collect the      | given |
valuesforeachvariablefrombothbackgroundin-
Wrong Inference
|     | Wrong Relations |     | formationandquestions,wherethesevaluesindi- |     |     |     |     |     |
| --- | --------------- | --- | ------------------------------------------- | --- | --- | --- | --- | --- |
Wrong Conclusion
|     |     |     | catewhetherspecificeventsoccurornot. |     |     |     | Crucially, |     |
| --- | --- | --- | ------------------------------------ | --- | --- | --- | ---------- | --- |
thisphasemaintainsstrictadherencetoexplicitly
Figure3: ErrorAnalysisofCausalCoT. stated information, avoiding any unsupported in-
ferencesorassumptionsinfavorofarigorousand
unbiaseddatacollectionprocess.
4 ProposedReasoningStrategy
4.2 Abduction
Asdiscussedinprevioussection,theprimarychal-
lenge for large language models is to minimize Thisphasefocusesoninferringtheposteriorcon-
incorrectinferences,whichareamajorsourceof straintsovertheexogenousnoisevariables,equiv-
errors. Toaddressthischallenge,weproposeCoIn alently, constraints over parent assignments that
(Counterfactual Inference), a systematic reason- make the observed factual world consistent with
ingframeworkthatguideslargelanguagemodels thestructuralequations. Foreachobservedvariable
throughstructuredproblem-solvinginsteadofre- V with value v , we invert its structural equa-
obs
lyingonintuitiveshortcutsormemorizedpatterns. tionV := f (Parents(V),U )toobtaineithera
|     |     |     |     | V   |     | V   |     |     |
| --- | --- | --- | --- | --- | --- | --- | --- | --- |
Our approach transforms counterfactual queries unique solution for U V or a feasible set over U V
into a five-phase algorithmic process, mirroring giventheparents. Indeterministiclogicalmodels,
how humans naturally approach “what if” ques- thisisoftenconvenientlycarriedoutbydeducing
tions (Sel et al., 2023): first understanding what parent assignments that must hold for v to be
obs
actuallyhappened,thenimaginingthealternative true. Theresultingvaluesarestoredasthefactual
scenario,systematicallyworkingthroughthecon- world knowledge base and will be held fixed in
sequences, andfinallydouble-checkingthelogic. subsequentInterventionActionandForwardInfer-
Thisstructuredapproachsignificantlyreducesrea- ence,ensuringcounterfactualsareevaluatedinthe
| soningerrorsbybreakingdowncomplexproblems  |     |     | sameworld. |     |     |     |     |     |
| ------------------------------------------ | --- | --- | ---------- | --- | --- | --- | --- | --- |
| intomanageablestepswithbuilt-invalidation. |     | An  |            |     |     |     |     |     |
4.3 InterventionAction
exampleofproposedparadigmisprovidedinAp-
| pendixA. |     |     | In this phase, | the framework |     | applies | the counter- |     |
| -------- | --- | --- | -------------- | ------------- | --- | ------- | ------------ | --- |
TheCoInframeworkconsistsoffivekeyphases: factualinterventionsdescribedinthequery. This
Extraction: ExtractCounterfactualInformation involvesmodifyingtheoriginalsetofcausalrules
from the given natural language facts. Abduc- byreplacingtheequationsfortheintervenedvari-
tion: Infer the underlying conditions from ob- ableswithconstantvalues,resultinginanupdated
servedfacts;InterventionAction: Applythehy- setofrules. Theinterventionsareincorporatedinto
potheticalchangesspecifiedinthequery;Forward theknowledgebase,effectivelymakingaprecise
Inference: Systematicallytracethroughthecausal alterationtothecausalgraph. Thisphasecaptures
consequences;Back-trackingValidation: Verify thecore“whatif”elementofthequery,allowing
thelogicalconsistencyoftheentirereasoningchain. theframeworktosimulatehypotheticalworldsin

a controlled way. It focuses on specific changes, Model Standard CausalCoTSolver Ours
whichstreamlinestheexplorationbylimitingthe
|     |     |     |     |     |     |     | GPT-3(Davinci-002) |     |     | 51.9 | 49.3 | 50.1 | 49.6 |
| --- | --- | --- | --- | --- | --- | --- | ------------------ | --- | --- | ---- | ---- | ---- | ---- |
search to paths directly affected by the interven- GPT-3 (Babbage- 49.6 9.8 47.9 45.8
002)
| tion, similar |     | to how | efficient |     | searches | eliminate |            |     |     |      |      |      |      |
| ------------- | --- | ------ | --------- | --- | -------- | --------- | ---------- | --- | --- | ---- | ---- | ---- | ---- |
|               |     |        |           |     |          |           | GPT-4omini |     |     | 50.4 | 59.8 | 47.2 | 79.9 |
unnecessarybranches.
|                      |     |     |     |     |     |     | GPT-4o            |     |     | 52.8 | 75.8 | 51.4 | 89.4 |
| -------------------- | --- | --- | --- | --- | --- | --- | ----------------- | --- | --- | ---- | ---- | ---- | ---- |
|                      |     |     |     |     |     |     | GPT-3.5turbo      |     |     | 50.6 | 49.1 | 49.6 | 58.9 |
| 4.4 ForwardInference |     |     |     |     |     |     | Claude-3(Sonnet)  |     |     | 51.6 | 59.0 | 51.8 | 89.8 |
|                      |     |     |     |     |     |     | Claude-3.5(Haiku) |     |     | 39.8 | 64.2 | 48.3 | 79.1 |
Duringthisiterativephase,theframeworkpredicts Gemini-1.5-flash 68.0 71.0 52.8 89.9
|     |     |     |     |     |     |     | Gemini-1.5-flash-8b |     |     | 50.4 | 64.8 | 50.3 | 83.9 |
| --- | --- | --- | --- | --- | --- | --- | ------------------- | --- | --- | ---- | ---- | ---- | ---- |
valuesforunobservedvariablesbyselectingnodes
|     |     |     |     |     |     |     | Deepseek-V3 |     |     | 51.9 | 74.2 | 49.3 | 91.8 |
| --- | --- | --- | --- | --- | --- | --- | ----------- | --- | --- | ---- | ---- | ---- | ---- |
inthecausalgraphwhoseparentvariablesareal-
ready known in the knowledge base and evaluat- Table3: ModelaccuracyonCounterBench. Wereport
ing their updated equations. Beginning with the theaverageaccuracyforfourinferencestrategies: Stan-
intervenedvariablesandtheinferrednoiseterms, dard,CausalCoT,Solver,andCoIn.
| it gradually                               | computes |     | the | effects | on  | downstream |     |     |     |     |     |     |     |
| ------------------------------------------ | -------- | --- | --- | ------- | --- | ---------- | --- | --- | --- | --- | --- | --- | --- |
| variablesuntilitreachesthetargetvariableY. |          |     |     |         |     | Ifa        |     |     |     |     |     |     |     |
approachcombinesLLMswithStructuralCausal
node’svaluecannotbecalculatedduetomissingin-
Model(SCM)tools(Pearl,2009)forcausalinfer-
formationaboutitsparents,theframeworkchooses
ence. ThestudyintroducesCausalTool,asuiteof
| another | suitable | node | and | continues |     | the process |     |     |     |     |     |     |     |
| ------- | -------- | ---- | --- | --------- | --- | ----------- | --- | --- | --- | --- | --- | --- | --- |
10inferencetoolsdesignedforvariouscausaltasks.
| until Y | is determined. |     | This | forward |     | progression |     |     |     |     |     |     |     |
| ------- | -------------- | --- | ---- | ------- | --- | ----------- | --- | --- | --- | --- | --- | --- | --- |
ItleveragesLLMstoclassifycausalquestions,ex-
mimicsadepth-firstexplorationofcausalchains,
tractcausalgraphsandformalizeddata,androute
enablingtheframeworktodynamicallyconstruct
|            |           |             |           |              |     |             | them to                           | the appropriate |     | tools | for | inference, | with   |
| ---------- | --------- | ----------- | --------- | ------------ | --- | ----------- | --------------------------------- | --------------- | --- | ----- | --- | ---------- | ------ |
| and assess | potential |             | outcomes. |              | By  | focusing on |                                   |                 |     |       |     |            |        |
|            |           |             |           |              |     |             | thefinalanswergeneratedbytheLLM.1 |                 |     |       |     |            | During |
| nodes that | can       | be computed |           | immediately, |     | it nav-     |                                   |                 |     |       |     |            |        |
inference,thetemperatureissettozero.
| igates the | dependency   |     | graph | efficiently, |           | steering |     |     |     |     |     |     |     |
| ---------- | ------------ | --- | ----- | ------------ | --------- | -------- | --- | --- | --- | --- | --- | --- | --- |
| clear of   | unproductive |     | paths | and          | promoting | a me-    |     |     |     |     |     |     |     |
5.2 MainResult
| thodical | advancement |     | toward |     | the solution. | The |     |     |     |     |     |     |     |
| -------- | ----------- | --- | ------ | --- | ------------- | --- | --- | --- | --- | --- | --- | --- | --- |
detailsofthisphaseisintheAppendixG. The comprehensive performance comparison
|     |     |     |     |     |     |     | across all | models | is  | presented | in  | Table | 3. Our |
| --- | --- | --- | --- | --- | --- | --- | ---------- | ------ | --- | --------- | --- | ----- | ------ |
4.5 Back-trackingValidation approachdemonstratesnotableimprovementsover
|            |     |          |           |     |        |           | existing | methods | across |     | the model | spectrum, |     |
| ---------- | --- | -------- | --------- | --- | ------ | --------- | -------- | ------- | ------ | --- | --------- | --------- | --- |
| To confirm |     | that the | predicted |     | values | are logi- |          |         |        |     |           |           |     |
callyconsistent,thisfinalphaseretracesthesteps with particularly noteworthy performance gains
|         |               |     |      |     |              |     | achieved | by smaller |     | language | models, | including |     |
| ------- | ------------- | --- | ---- | --- | ------------ | --- | -------- | ---------- | --- | -------- | ------- | --------- | --- |
| through | the knowledge |     | base | and | re-evaluates | the |          |            |     |          |         |           |     |
GPT-4omini,Claude-3.5Haiku,andGemini-1.5-
equationforeachnon-noisevariableusingthepre-
|               |     |                                  |     |     |     |     | flash-8b. | Forinstance,ourmethodenablesGPT-4o |     |     |     |     |     |
| ------------- | --- | -------------------------------- | --- | --- | --- | --- | --------- | ---------------------------------- | --- | --- | --- | --- | --- |
| dictedvalues. |     | ForeverysuchvariableV,itrecalcu- |     |     |     |     |           |                                    |     |     |     |     |     |
minitoachieveanaccuracyof79.9%,surpassing
latestheexpectedvaluebasedontheupdatedequa-
theperformanceofseverallargermodelswithout
tionandchecksifitmatchesthepreviouslystored
|     |     |     |     |     |     |     | CoInenhancement. |     | AsdetailedinTable4,taking |     |     |     |     |
| --- | --- | --- | --- | --- | --- | --- | ---------------- | --- | ------------------------- | --- | --- | --- | --- |
value. Ifanymismatchoccurs,theframeworksig-
nalsanerror,highlightingapotentialissueinthe GPT-4ominiasanexample,CoInachievessuperior
performanceacrossallfivetypesofcounterfactual
| earlierreasoningthatmayneedreevaluation. |        |     |              |     |         | This    |            |      |              |     |        |         |        |
| ---------------------------------------- | ------ | --- | ------------ | --- | ------- | ------- | ---------- | ---- | ------------ | --- | ------ | ------- | ------ |
|                                          |        |     |              |     |         |         | questions, | with | particularly |     | better | results | on ba- |
| validation                               | serves | as  | a protective |     | measure | against |            |      |              |     |        |         |        |
sicquestionscomparedtomorecomplexvariants.
| errors that | could | accumulate |     | during |     | the process, |               |                                |     |     |     |     |     |
| ----------- | ----- | ---------- | --- | ------ | --- | ------------ | ------------- | ------------------------------ | --- | --- | --- | --- | --- |
|             |       |            |     |        |     |              | Additionally, | state-of-the-artLLMssuchasGPT- |     |     |     |     |     |
akintoretracingapathtoconfirmitsvalidity.
4o,Gemini-1.5-flash,andDeepseek-V3achievere-
| 5 Experiments |     |     |     |     |     |     | markableaccuracyapproachingorexceeding90% |     |     |     |     |             |     |
| ------------- | --- | --- | --- | --- | --- | --- | ----------------------------------------- | --- | --- | --- | --- | ----------- | --- |
|               |     |     |     |     |     |     | whenaugmentedwithourmethod.               |     |     |     |     | TakenGPT-4o |     |
5.1 ExperimentSetup as example, Our strategy improves the accuracy
WeadoptedthesameLLMsasmentionedinSec- ofthemodelfrom75.8%to89.4%,demonstrating
tion3forourexperiments. Toestablishbaselines, CoIn’seffectivenessinguidingLLMsthroughal-
|     |     |     |     |     |     |     | gorithmtoexplorepathsstep-by-step. |     |     |     |     | Theresults |     |
| --- | --- | --- | --- | --- | --- | --- | ---------------------------------- | --- | --- | --- | --- | ---------- | --- |
weimplementedbothCausalCoT(Jinetal.,2023)
| andstandardsolverstrategies. |     |     |     | Thelatterintegrates |     |     |     |     |     |     |     |     |     |
| ---------------------------- | --- | --- | --- | ------------------- | --- | --- | --- | --- | --- | --- | --- | --- | --- |
1SincethesourcecodeforCausalToolisnotpubliclyavail-
externaltoolsintothechain-of-thoughtprocess,as
able,were-implementeditscounterfactualinferenceproce-
described in (Hua et al., 2024). Specifically, this durebasedondescriptionsintheoriginalpaper.

Methods Basic Cond. Joint Nested Back. Avg. terfactualreasoningtasks.
Standard 50.0 50.0 50.0 50.0 52.5 50.4
90
CausalCoT 57.2 66.4 60.0 63.2 50.0 59.8
Solver 35.2 54.4 50.4 50.0 45.5 47.2 80
Ours 82.8 79.2 80.0 80.4 76.5 79.9 70
60
Table 4: Accuracy of GPT-4o mini across five query
50
typesintheCounterBench.
40
30
indicatethatcontemporaryLLMs,whenequipped 20
withourstrategy,caneffectivelyresolvemostfor- 10
malcomplexcounterfactualproblems. Thedetails 0
gemini-1.5 gemini-1.5 gemini-1.5-8bgemini-1.5-8b
ofallperformanceofourresultsarepresentedin anti- common- anti- common-
commonsense sense commonsense sense
Appendix C. Moreover, in Appendix D, we con-
ductederroranalysis. Theanalysisrevealsasub-
stantial reduction in errors of inference process.
Moreover,wealsoexaminetheimpactofcomplex
causal relationships on outcomes. We found that
accuracy decreases as the number of variants in-
creasesforCausalCoTandCoIn. Thedetailsare
showninthenextsection.
5.3 ValidatingGeneralizationAbility
Inthissection, weevaluatethegeneralizationca-
pabilityofCoInusingtheCLADDERdataset(Jin
etal.,2023). CLADDERisadatasetfocusonthe
causalreasoningquestions. WeutilizetheCLAD-
DERdatasettodetermineiftheproposedmethod
canbeextendedbeyondtheCounterBenchdataset.
Unlikeourdataset,whichfocusesonformalrules,
CLADDER includes examples that utilize com-
monsenseknowledgeratherthancausalinference
abilitiestoanswerqueries. Specifically,itencom-
passesbothcommonsenseandanti-commonsense
scenarios, allowing us to explore whether CoIn
remains effective under the influence of pretrain-
ingknowledgeinLLMs. Weconductexperiments
on the counterfactual subset of CLADDER. We
applied the Gemini-1.5 and Gemini-1.5-8b mod-
elstobothcommonsenseandanti-commonsense
queries,withtheresultsdisplayedinFigure4and
detailed examples in Appendix E. These results
demonstratethatperformanceisconsistentlystable
across different reasoning paradigms, suggesting
that pretraining knowledge has a limited impact
ontheCoIncounterfactualreasoningcapabilities.
Furthermore,ourmethodachievesanaccuracyof
78.98%,outperformingbothCausalCoTat64.77%
andtheStandardmethodat64.20%. Thisperfor-
manceunderscoresCoIn’sgeneralizabilityandits
potential for broader application in various coun-
)%(
ycaruccA
Standard
CausalCoT
Ours
Figure 4: Accuracy comparison between Standard,
CoIn, and CausalCoT method in Anti-commonsense
andCommonsenseDataset.
6 RelatedWork
CounterfactualReasoning. Counterfactualrea-
soning explores how outcomes change when cer-
tainvariablesarealteredfromtheirhistoricalstates.
InStructuralCausalModels(SCMs),Pearl’s(Pearl,
2009) “surgery” and do-calculus provide system-
aticwaystoinferinterventionoutcomes,highlight-
ing deep causal knowledge required for accurate
inference. Counterfactuals can be deterministic
or probabilistic: deterministic settings yield pre-
dictable outcomes from given conditions, while
probabilistic models incorporate inherent uncer-
tainties. These methods have gained traction in
domains like social sciences, where they assess
alternativepolicyoutcomesandstudycausalmech-
anismsinobservationaldata(Morgan,2015),and
inmedicine,wheretheyenablepersonalizedtreat-
mentanddecisionsupport(Johanssonetal.,2016;
Shalitetal.,2017;Louizosetal.,2017;Yoonetal.,
2018). Inartificialintelligence,counterfactualrea-
soning is crucial for interpretability and fairness,
enablingmodelstogeneratealternativescenarios
andassessdecision-makingrobustness. Although
recent efforts extend counterfactual reasoning to
LLMs(Jinetal.,2023),significantchallengesper-
sist,particularlyregardingcomplexvariablerela-
tionships in high-dimensional text data. Conse-
quently,bridgingthegapbetweentextualcomplex-
ityandrobustcausalinferenceremainsafocalpoint
forfutureresearch.
LLMs in Counterfactual Learning. With the
rapidevolutionofLLMs,theresearchcommunity

hasincreasinglyfocusedontheirabilitytoperform Sébastien Bubeck, Varun Chandrasekaran, Ronen El-
causalinference(Zhangetal.,2023;Ashwanietal., dan, Johannes Gehrke, Eric Horvitz, Ece Kamar,
|     |     |     |     |     |     |     | Peter Lee, | Yin Tat | Lee, | Yuanzhi | Li, Scott | Lund- |
| --- | --- | --- | --- | --- | --- | --- | ---------- | ------- | ---- | ------- | --------- | ----- |
2024). AprominentexampleisCausalAgent,an
|     |     |     |     |     |     |     | berg,etal.2023. |     | Sparksofartificialgeneralintelli- |     |     |     |
| --- | --- | --- | --- | --- | --- | --- | --------------- | --- | --------------------------------- | --- | --- | --- |
agent-basedLLMframeworkthatmergesanLLM
|             |       |     |         |       |      |         | gence: Earlyexperimentswithgpt-4. |     |     |     | arXivpreprint |     |
| ----------- | ----- | --- | ------- | ----- | ---- | ------- | --------------------------------- | --- | --- | --- | ------------- | --- |
| with causal | tools | for | complex | tasks | (Han | et al., |                                   |     |     |     |               |     |
arXiv:2303.12712.
| 2024). | While it | excels | at identifying |     | causal | asso- |     |     |     |     |     |     |
| ------ | -------- | ------ | -------------- | --- | ------ | ----- | --- | --- | --- | --- | --- | --- |
IviChatzi,NinaCorveloBenz,EleniStraitouri,Stratis
| ciations | and conducting |     | interventions, |     |     | it largely |                                         |     |     |     |     |       |
| -------- | -------------- | --- | -------------- | --- | --- | ---------- | --------------------------------------- | --- | --- | --- | --- | ----- |
|          |                |     |                |     |     |            | Tsirtsis,andManuelGomez-Rodriguez.2024. |     |     |     |     | Coun- |
omitscounterfactualreasoning,limitingitsapplica- terfactualtokengenerationinlargelanguagemodels.
bilitytomoreadvancedscenarios. Currentefforts arXivpreprintarXiv:2409.17027.
| to integrate | counterfactual |     |     | reasoning | into | LLMs |     |     |     |     |     |     |
| ------------ | -------------- | --- | --- | --------- | ---- | ---- | --- | --- | --- | --- | --- | --- |
HuigangChen,TotteHarinen,Jeong-YoonLee,Mike
| typically | follow | two | paths. | First, | commonsense- |     |           |        |       |                 |     |        |
| --------- | ------ | --- | ------ | ------ | ------------ | --- | --------- | ------ | ----- | --------------- | --- | ------ |
|           |        |     |        |        |              |     | Yung, and | Zhenyu | Zhao. | 2020. Causalml: |     | Python |
basedapproachesleveragebackgroundknowledge
|             |            |         |           |             |         |          | packageforcausalmachinelearning. |             |     |                     | arXivpreprint |     |
| ----------- | ---------- | ------- | --------- | ----------- | ------- | -------- | -------------------------------- | ----------- | --- | ------------------- | ------------- | --- |
| to imagine  | scenarios  |         | that defy | established |         | facts    | arXiv:2002.11631.                |             |     |                     |               |     |
| (Ning et    | al., 2024; | Chatzi  | et        | al.,        | 2024;   | Musi and |                                  |             |     |                     |               |     |
|             |            |         |           |             |         |          | DeepSeek.2024.                   | DeepSeek:   |     | AI-PoweredSearchEn- |               |     |
| Palmieri,   | 2024;      | Vicuna, | 2023),    | such        | as      | positing |                                  |             |     |                     |               |     |
|             |            |         |           |             |         |          | gine. Accessed:                  | 2025-02-15. |     |                     |               |     |
| alternative | historical |         | outcomes. |             | Second, | graph-   |                                  |             |     |                     |               |     |
based methods employ formal causal graphs and AmirFeder,KatherineAKeith,EmaadManzoor,Reid
Pryzant,DhanyaSridhar,ZachWood-Doughty,Jacob
externalPythonpackagesforcomputations,asseen
Eisenstein,JustinGrimmer,RoiReichart,MargaretE
| inCausalTool(Huaetal.,2024). |     |     |     |     | Althoughthese |     |                    |     |                              |     |     |     |
| ---------------------------- | --- | --- | --- | --- | ------------- | --- | ------------------ | --- | ---------------------------- | --- | --- | --- |
|                              |     |     |     |     |               |     | Roberts,etal.2022. |     | Causalinferenceinnaturallan- |     |     |     |
methodseffectivelyincorporatestructuredcausal
|     |     |     |     |     |     |     | guageprocessing: |     | Estimation,prediction,interpreta- |     |     |     |
| --- | --- | --- | --- | --- | --- | --- | ---------------- | --- | --------------------------------- | --- | --- | --- |
information, they often offload key calculations tionandbeyond. TransactionsoftheAssociationfor
ComputationalLinguistics,10:1138–1158.
outsidetheLLM.
|              |     |     |     |     |     |     | Google. 2024.   | Gemini.     |     | https://gemini.google. |     |     |
| ------------ | --- | --- | --- | --- | --- | --- | --------------- | ----------- | --- | ---------------------- | --- | --- |
| 7 Conclusion |     |     |     |     |     |     | com/. Accessed: | 2025-01-06. |     |                        |     |     |
Inthiswork,wedevelopandextendCounterBench, IanDGow,DavidFLarcker,andPeterCReiss.2016.
acounterfactualreasoningdatasetwithfiveprob- Causalinferenceinaccountingresearch. Journalof
AccountingResearch,54(2):477–523.
| lem types | for LLM | evaluation. |     |     | Our findings | re- |     |     |     |     |     |     |
| --------- | ------- | ----------- | --- | --- | ------------ | --- | --- | --- | --- | --- | --- | --- |
vealthatmostLLMsperformnear-randomly,with Emilia Gvozdenovic´, Lucio Malvisi, Elisa Cinconze,
StijnVansteelandt,PhoebeNakanwagi,Emmanuel
state-of-the-artmethodsshowingminimalimprove-
ment. To address these challenges, we propose Aris,andDominiqueRosillon.2021. Causalinfer-
enceconceptsappliedtothreeobservationalstudies
| CoIn, a | reasoning | paradigm |     | inspired | by  | formal |                                   |     |     |     |            |     |
| ------- | --------- | -------- | --- | -------- | --- | ------ | --------------------------------- | --- | --- | --- | ---------- | --- |
|         |           |          |     |          |     |        | inthecontextofvaccinedevelopment: |     |     |     | fromtheory |     |
causalinferenceprinciplesandplanningstrategies. to practice. BMC Medical Research Methodology,
| CoInguidesLLMsthroughiterativethinkingand |     |     |     |     |     |     | 21:1–10. |     |     |     |     |     |
| ----------------------------------------- | --- | --- | --- | --- | --- | --- | -------- | --- | --- | --- | --- | --- |
backtrackingtoexplorereasoningpathsmoreeffec-
KairongHan,KunKuang,ZiyuZhao,JunjianYe,and
tively. Ourapproachsignificantlyenhancescoun-
|     |     |     |     |     |     |     | FeiWu.2024. | Causalagentbasedonlargelanguage |     |     |     |     |
| --- | --- | --- | --- | --- | --- | --- | ----------- | ------------------------------- | --- | --- | --- | --- |
terfactualreasoningcapabilitiesofLLMs. model. arXivpreprintarXiv:2408.06849.
|     |     |     |     |     |     |     | Paul W Holland. | 1986. | Statistics |     | and causal | infer- |
| --- | --- | --- | --- | --- | --- | --- | --------------- | ----- | ---------- | --- | ---------- | ------ |
ence. JournaloftheAmericanstatisticalAssociation,
References
81(396):945–960.
| Alwin.                  | 2023. Understanding |     |     | causal     | ai: Bridging | the      |               |         |       |         |           |        |
| ----------------------- | ------------------- | --- | --- | ---------- | ------------ | -------- | ------------- | ------- | ----- | ------- | --------- | ------ |
|                         |                     |     |     |            |              |          | Zhenyang Hua, | Shuyue  | Xing, | Huixing | Jiang,    | Chen   |
| gap between             | correlation         |     | and | causation. |              | https:// |               |         |       |         |           |        |
|                         |                     |     |     |            |              |          | Wei, and      | Xiaojie | Wang. | 2024.   | Improving | causal |
| www.alwin.io/causal-ai. |                     |     |     | Accessed:  | 2025-01-06.  |          |               |         |       |         |           |        |
inferenceoflargelanguagemodelswithscmtools.
|     |     |     |     |     |     |     | In CCF International |     | Conference |     | on Natural | Lan- |
| --- | --- | --- | --- | --- | --- | --- | -------------------- | --- | ---------- | --- | ---------- | ---- |
Anthropic. 2024. Claude. https://www.anthropic. guage Processing and Chinese Computing, pages
| com/api. | Accessed: |     | 2025-01-06. |     |     |     |     |     |     |     |     |     |
| -------- | --------- | --- | ----------- | --- | --- | --- | --- | --- | --- | --- | --- | --- |
3–14.Springer.
Swagata Ashwani, Kshiteesh Hegde, Nishith Reddy Zhijing Jin, Yuen Chen, Felix Leeb, Luigi Gresele,
Mannuru, Dushyant Singh Sengar, Mayank Jindal, Ojasv Kamal, LYU Zhiheng, Kevin Blin, Fer-
Krishna Chaitanya Rao Kathala, Dishant Banga, nando Gonzalez Adauto, Max Kleiman-Weiner,
Vinija Jain, and Aman Chadha. 2024. Cause and Mrinmaya Sachan, et al. 2023. Cladder: Assess-
effect: Canlargelanguagemodelstrulyunderstand ingcausalreasoninginlanguagemodels. InThirty-
causality? InProceedingsoftheAAAISymposium seventhconferenceonneuralinformationprocessing
| Series,volume4,pages2–9. |     |     |     |     |     |     | systems. |     |     |     |     |     |
| ------------------------ | --- | --- | --- | --- | --- | --- | -------- | --- | --- | --- | --- | --- |

FredrikJohansson,UriShalit,andDavidSontag.2016. JingMa.2024. Causalinferencewithlargelanguage
Learningrepresentationsforcounterfactualinference. model: Asurvey. arXivpreprintarXiv:2409.09822.
| In International | conference |     | on machine | learning, |     |     |     |     |     |     |
| ---------------- | ---------- | --- | ---------- | --------- | --- | --- | --- | --- | --- | --- |
pages3020–3029.PMLR. SL Morgan. 2015. Counterfactuals and causal infer-
ence. CambridgeUniversityPress.
| AtoosaKasirzadehandAndrewSmart.2021. |     |     |     | Theuse |     |     |     |     |     |     |
| ------------------------------------ | --- | --- | --- | ------ | --- | --- | --- | --- | --- | --- |
and misuse of counterfactuals in ethical machine Elena Musi and Rudi Palmieri. 2024. The fallacy of
learning. InProceedingsofthe2021ACMConfer- explainablegenerativeai: evidencefromargumenta-
enceonFairness,Accountability,andTransparency, tivepromptingintwodomains. InCEURWorkshop
| pages228–236. |     |     |     |     | Proceedings,volume3769,pages59–69. |       |      |        |       |            |
| ------------- | --- | --- | --- | --- | ---------------------------------- | ----- | ---- | ------ | ----- | ---------- |
|               |     |     |     |     | Xuefei Ning,                       | Zinan | Lin, | Zixuan | Zhou, | Zifu Wang, |
EmreKıcıman,RobertNess,AmitSharma,andChen-
haoTan.2023. Causalreasoningandlargelanguage HuazhongYang,andYuWang.2024. Skeleton-of-
models: Openinganewfrontierforcausality. arXiv thought: Promptingllmsforefficientparallelgener-
preprintarXiv:2305.00050. ation. In The Twelfth International Conference on
LearningRepresentations.
LisaKoonce,KarenKNelson,andCatherineMShake-
speare. 2011. Judging the relevance of fair value OpenAI.2024. Models. https://platform.openai.
for financial instruments. The Accounting Review, com/docs/models. Accessed: 2025-01-06.
86(6):2075–2098.
|                                                 |     |          |                 |     | Judea Pearl. | 2009. | Causality. |     | Cambridge | university |
| ----------------------------------------------- | --- | -------- | --------------- | --- | ------------ | ----- | ---------- | --- | --------- | ---------- |
| ParthasarathyKrishnamurthyandAnuradhaSivaraman. |     |          |                 |     | press.       |       |            |     |           |            |
| 2002. Counterfactual                            |     | thinking | and advertising | re- |              |       |            |     |           |            |
sponses. JournalofConsumerResearch,28(4):650– JudeaPearlandDanaMackenzie.2018. Thebookof
|      |     |     |     |     | why: | the new | science | of cause | and | effect. |
| ---- | --- | --- | --- | --- | ---- | ------- | ------- | -------- | --- | ------- |
| 658. |     |     |     |     |      |         |         |          |     | Basic   |
books.
| Evangelia Kyrimi, | Somayyeh |     | Mossadegh, | Jared M |     |     |     |     |     |     |
| ----------------- | -------- | --- | ---------- | ------- | --- | --- | --- | --- | --- | --- |
Wohlgemut, RebeccaSStoner, NigelRMTai, and Fabio Petroni, Tim Rocktäschel, Patrick Lewis, An-
WilliamMarsh.2025. Counterfactualreasoningus- tonBakhtin,YuxiangWu,AlexanderHMiller,and
ingcausalbayesiannetworksasahealthcaregover- SebastianRiedel.2019. Languagemodelsasknowl-
arXivpreprintarXiv:1909.01066.
| nancetool. InternationalJournalofMedicalInfor- |     |     |     |     | edgebases? |     |     |     |     |     |
| ---------------------------------------------- | --- | --- | --- | --- | ---------- | --- | --- | --- | --- | --- |
matics,193:105681.
|     |     |     |     |     | Neil Sahota. |     | 2023. | Causal |     | ai: Bridging |
| --- | --- | --- | --- | --- | ------------ | --- | ----- | ------ | --- | ------------ |
Jia Li and Xiang Li. 2024. Relation-first modeling the gap between correlation and causation.
paradigmforcausalrepresentationlearningtoward https://www.neilsahota.com. Accessed: 2025-01-
| thedevelopmentofagi. |     | Preprint,arXiv:2307.16387. |     |     | 06. |     |     |     |     |     |
| -------------------- | --- | -------------------------- | --- | --- | --- | --- | --- | --- | --- | --- |
Weixin Liang, Yaohui Zhang, Zhengxuan Wu, Haley Bilgehan Sel, Ahmad Al-Tawaha, Vanshaj Khattar,
Lepp,WenlongJi,XuandongZhao,HanchengCao, Ruoxi Jia, and Ming Jin. 2023. Algorithm of
ShengLiu,SiyuHe,ZhiHuang,etal.2024. Mapping thoughts: Enhancing exploration of ideas in large
theincreasinguseofllmsinscientificpapers. arXiv languagemodels. arXivpreprintarXiv:2308.10379.
preprintarXiv:2404.01268.
|     |     |     |     |     | Uri Shalit, | Fredrik | D Johansson, |     | and | David Sontag. |
| --- | --- | --- | --- | --- | ----------- | ------- | ------------ | --- | --- | ------------- |
JinxinLiu,ShulinCao,JiaxinShi,TingjianZhang,Lun- 2017. Estimating individual treatment effect: gen-
yiuNie,LinmeiHu,LeiHou,andJuanziLi.2024a. eralizationboundsandalgorithms. InInternational
Howproficientarelargelanguagemodelsinformal conferenceonmachinelearning,pages3076–3085.
| languages? anin-depthinsightforknowledgebase |     |                            |     |     | PMLR. |     |     |     |     |     |
| -------------------------------------------- | --- | -------------------------- | --- | --- | ----- | --- | --- | --- | --- | --- |
| questionanswering.                           |     | InFindingsoftheAssociation |     |     |       |     |     |     |     |     |
forComputationalLinguisticsACL2024,pages792– Amit Sharma and Emre Kiciman. 2020. Dowhy:
| 815. |     |     |     |     | An end-to-end |     | library | for causal | inference. | arXiv |
| ---- | --- | --- | --- | --- | ------------- | --- | ------- | ---------- | ---------- | ----- |
preprintarXiv:2011.04216.
XiaoyuLiu,PaihengXu,JundaWu,JiaxinYuan,Yifan
Yang,YuhangZhou,FuxiaoLiu,TianruiGuan,Hao- ArturTarassow.2023. Thepotentialofllmsforcoding
liangWang,TongYu,etal.2024b. Largelanguage withlow-resourceanddomain-specificprogramming
modelsandcausalinferenceincollaboration: Acom- languages. arXivpreprintarXiv:2307.13018.
| prehensivesurvey. | arXivpreprintarXiv:2403.09606. |     |     |     |         |       |         |                |     |             |
| ----------------- | ------------------------------ | --- | --- | --- | ------- | ----- | ------- | -------------- | --- | ----------- |
|                   |                                |     |     |     | Vicuna. | 2023. | Vicuna: | An open-source |     | chatbot im- |
MassimoLoiandMargaridaRodrigues.2012. Anote pressingGPT-4with90%*ChatGPTquality. https:
ontheimpactevaluationofpublicpolicies: thecoun- //vicuna.lmsys.org/. Accessed: 2023.
terfactualanalysis.
JasonWei,XuezhiWang,DaleSchuurmans,Maarten
ChristosLouizos,UriShalit,JorisMMooij,DavidSon- Bosma,FeiXia,EdChi,QuocVLe,DennyZhou,
tag,RichardZemel,andMaxWelling.2017. Causal etal.2022. Chain-of-thoughtpromptingelicitsrea-
effectinferencewithdeeplatent-variablemodels. Ad- soninginlargelanguagemodels. Advancesinneural
vancesinneuralinformationprocessingsystems,30. informationprocessingsystems,35:24824–24837.

Jinsung Yoon, James Jordon, and Mihaela Van lemsofsufficientcomplexitytoeffectivelyevaluate
Der Schaar. 2018. Ganite: Estimation of individ- counterfactualreasoningabilitiesofmodels. The
ualizedtreatmenteffectsusinggenerativeadversarial
|     |     |     |     |     | inter-annotator |     | agreement |     | between | the | two PhD |
| --- | --- | --- | --- | --- | --------------- | --- | --------- | --- | ------- | --- | ------- |
nets. InInternationalconferenceonlearningrepre-
annotatorswasapproximately95%,demonstrating
sentations.
|     |     |     |     |     | strongconsistencyintheirjudgments. |     |     |     |     |     | Beforethe |
| --- | --- | --- | --- | --- | ---------------------------------- | --- | --- | --- | --- | --- | --------- |
MatejZecˇevic´,MoritzWillig,DevendraSinghDhami,
|                           |     |                |     |       | full annotation |     | began, | both | annotators |     | were pro- |
| ------------------------- | --- | -------------- | --- | ----- | --------------- | --- | ------ | ---- | ---------- | --- | --------- |
| andKristianKersting.2023. |     | Causalparrots: |     | Large |                 |     |        |      |            |     |           |
videdwithasetofpracticeexamplesanddetailed
languagemodelsmaytalkcausalitybutarenotcausal.
arXivpreprintarXiv:2308.13067. reasoning guidelines. They participated in a cali-
brationphaseinvolvingdiscussionandalignment
| Cheng Zhang, | Stefan Bauer, | Paul | Bennett, | Jiangfeng |     |     |     |     |     |     |     |
| ------------ | ------------- | ---- | -------- | --------- | --- | --- | --- | --- | --- | --- | --- |
onannotationstandards,ensuringasharedunder-
| Gao, Wenbo | Gong, Agrin | Hilmkil, | Joel | Jennings, |     |     |     |     |     |     |     |
| ---------- | ----------- | -------- | ---- | --------- | --- | --- | --- | --- | --- | --- | --- |
ChaoMa,TomMinka,NickPawlowski,etal.2023. standingofthetask. Thispreparatorystephelped
establishconsistencyandreliabilityacrossthefull
| Understanding    | causality          | with large | language | mod-     |          |     |     |     |     |     |     |
| ---------------- | ------------------ | ---------- | -------- | -------- | -------- | --- | --- | --- | --- | --- | --- |
| els: Feasibility | and opportunities. |            | arXiv    | preprint | dataset. |     |     |     |     |     |     |
arXiv:2304.05524.
C.MoreExperimentDetails
Appendix
|     |     |     |     |     | Table 5 | presents | a   | comprehensive |     | performance |     |
| --- | --- | --- | --- | --- | ------- | -------- | --- | ------------- | --- | ----------- | --- |
A.MethodPromptDesign
|     |     |     |     |     | comparison | between |     | the Solver |     | method | and our |
| --- | --- | --- | --- | --- | ---------- | ------- | --- | ---------- | --- | ------ | ------- |
Ourpromptdesign,asillustratedinFigure5,has CoInapproachacrossvariousmodelsontheCoun-
|     |     |     |     |     | terBenchdataset. |     | Ouranalysisrevealsseveralsig- |     |     |     |     |
| --- | --- | --- | --- | --- | ---------------- | --- | ----------------------------- | --- | --- | --- | --- |
beencarefullystructuredtooptimizetheinteraction
betweenouralgorithmandLargeLanguageMod- nificantpatternsinmodelperformanceacrossdif-
els (LLMs). At its core, the design incorporates ferent counterfactual reasoning tasks. First and
multiplefew-shotexamplesthatserveascompre- foremost,CoIndemonstratesconsistentsuperiority
hensive demonstrations of our algorithm’s opera- over the Solver method across all task categories
tionalframework. Theseexamplesarestrategically andmodelarchitectures. Thisimprovementispar-
selected to showcase various reasoning patterns ticularlypronouncedinnewermodelarchitectures,
withstate-of-the-artmodelslikeGPT-4o,Claude-3
andproblem-solvingapproaches,providingLLMs
witharobustfoundationforunderstandingthealgo- (Sonnet), and Gemini-1.5-flash showing remark-
rithm’smethodology. Withintheprompt,wehave ableperformancegains. Notably,GPT-4oachieves
perfectaccuracy(100.0%)onbasicreasoningtasks
meticulouslydetailedstep-by-stepinstructions,cre-
atingaclearandstructuredinformationflowthat underourmethod. Deepseek-V3demonstratesex-
guides the model through the reasoning process. ceptionalconsistencywithhighperformanceacross
ThisstructuredapproachleveragesLLMs’inherent all task types. Its accuracy comes to 99.6% for
|     |     |     |     |     | basic tasks | and | maintaining |     | above | 90% | average |
| --- | --- | --- | --- | --- | ----------- | --- | ----------- | --- | ----- | --- | ------- |
in-contextlearningcapabilities,enablingthemto
systematically explore solution paths rather than accuracy. Theperformancedistributionacrossdif-
relyingonintuitiveresponses. Thisapproachnot ferenttasktypesrevealsinterestingpatterns. Basic
|               |             |         |          |      | reasoning | tasks | consistently |     | yield | the | highest ac- |
| ------------- | ----------- | ------- | -------- | ---- | --------- | ----- | ------------ | --- | ----- | --- | ----------- |
| only enhances | the model’s | ability | to break | down |           |       |              |     |       |     |             |
problems and evaluate paths efficiently but also curacy under our method, particularly evident in
reducingthelikelihoodofgeneratingerroneousin- largermodels. However,thiscategoryalsoexhibits
termediatestepsandimprovingreasoningstability. themostsignificantperformancevariationacross
|     |     |     |     |     | different | model | architectures, |     | suggesting |     | that ba- |
| --- | --- | --- | --- | --- | --------- | ----- | -------------- | --- | ---------- | --- | -------- |
siccounterfactualreasoningcapabilitiesarehighly
B.HumanEvaluation
|     |     |     |     |     | sensitive | to model | scale | and | architecture. |     | In con- |
| --- | --- | --- | --- | --- | --------- | -------- | ----- | --- | ------------- | --- | ------- |
Toassessthequalityofourdataset,weaskedtwo trast, joint reasoning tasks show relatively stable
Ph.D. students with expertise in causal inference performance across different models, indicating
toanswer200randomlyselectedquestions. They thatthesecapabilitiesmaybemorefundamentally
achieved an average accuracy of 97.75% and re- tiedtothereasoningframeworkratherthanmodel
quiredfourhourstocompletethem,reflectingthe size. Moreover,weobserveaclearcorrelationbe-
substantial cognitive effort involved. According tweenmodelrecencyandperformance,withnewer
toparticipantfeedback,thesequestionsdemanded modelslikeGPT-4oandClaude-3(Sonnet)achiev-
carefulconsiderationofmultiplecausalfactorsand ingsignificantlyhigheraverageaccuracies(89.8%,
explicitcounterfactualreasoningsteps. Thesefind- 89.4%)comparedtotheirpredecessors. Thistrend
ings demonstrate that our dataset presents prob- holdstrueacrossalltasktypes,thoughthemagni-

tudeofimprovementvariesbycategory. Thecon- in Figure 12, the approach breaks down the rea-
sistent performance improvements across newer soningprocessintodistinctphases: counterfactual
modelarchitecturessuggestthatrecentadvancesin informationcollection,andsystematicexploration
languagemodeldevelopmenthaveenhancedtheir ofinferencepaths. Thisstructureddecomposition
capacity for structured counterfactual reasoning contrastssharplywiththestandardapproachshown
whencombinedwithourmethodology. inFigure9,whichprovidesminimalguidancefor
|     |     |     |     |     |     | navigatingthereasoningprocess. | Throughexplicit |     |
| --- | --- | --- | --- | --- | --- | ------------------------------ | --------------- | --- |
D.ErrorAnalysiscomparisonbetweenOur
variablemappingandsystematicpathexploration,
MethodandCausalCoT
|     |     |     |     |     |     | CoIn enables | models to systematically | evaluate |
| --- | --- | --- | --- | --- | --- | ------------ | ------------------------ | -------- |
By randomly sampling 50 instances and catego- possible causal chains, leading to more reliable
rizingerrorsintothreedistincttypes, wrongrela- andtraceableinferenceoutcomes. Thekeyreason
tions, wrong inferences, and wrong conclusions, why only CoIn arrived at the correct answer lies
we systematically evaluated the model’s perfor- initsexplicitstructuredreasoningprocess,which
mance. Theanalysisdemonstratednotablediffer- ensuresasystematicandrobustapproachtocoun-
ences in the relative distribution of errors, with terfactual inference. Unlike CausalCoT and the
inference-related errors decreasing from 86% to standardmethod,CoInemploysastep-by-stepal-
46%. This significant reduction combining with gorithmicframeworkthatsystematicallyprocesses
thediminishederrorquantitysubstantiatesanen- causaldependencies,preventingshortcutreasoning
| hanced               | counterfactual | inference | capability. |          | Con-   | andheuristicerrors. |     |     |
| -------------------- | -------------- | --------- | ----------- | -------- | ------ | ------------------- | --- | --- |
| currently,           | we also        | observed  | a relative  | increase | in     |                     |     |     |
| relationship-related |                | errors,   | 12% to      | 50%.     | Conse- |                     |     |     |
quently,theoveralleffectofourstrategyispositive
asthenumberoferrorscomedownnotably.
E.CLADDERDatasetExample
TwoexamplesaregeneratedfromtheCLADDER
| dataset. | ItisshowninFigure |     | 7andFigure8,are |     |     |     |     |     |
| -------- | ----------------- | --- | --------------- | --- | --- | --- | --- | --- |
designedtoevaluateamodel’sabilitytodistinguish
betweencommonsenseandanti-commonsenserea-
| soningincounterfactualscenarios. |         |        |               | Commonsense |       |     |     |     |
| -------------------------------- | ------- | ------ | ------------- | ----------- | ----- | --- | --- | --- |
| reasoning                        | follows | causal | relationships | that        | align |     |     |     |
G.ForwardInferenceAlgorithm
| with human | intuition | and | everyday | knowledge, |     |     |     |     |
| ---------- | --------- | --- | -------- | ---------- | --- | --- | --- | --- |
makingiteasierformodelstoinferoutcomesbased
| onfamiliarpatterns. |          | Incontrast,anti-commonsense |            |      |         |     |     |     |
| ------------------- | -------- | --------------------------- | ---------- | ---- | ------- | --- | --- | --- |
| reasoning           | presents | causal                      | structures | that | contra- |     |     |     |
dictintuitiveexpectations,requiringmodelstorely
solelyonexplicitlyprovidedcausalrelationships
| rather than | prior | knowledge. | By testing |     | both rea- |     |     |     |
| ----------- | ----- | ---------- | ---------- | --- | --------- | --- | --- | --- |
soningparadigms,theseexamplesassesswhether ThepartisforwardinferenceAlgorithm,thecore
amodelcanaccuratelydifferentiatebetweenintu- methodologicalcomponentthatsystematicallyap-
itiveandcounterintuitivecausalstructures,ensur- plies gathered information from previous Extrac-
ingthatreal-worldbiasesdonotinterferewithits tion, Abduction, andActionstepstoevaluatethe
counterfactualreasoningabilities. target event. The framework employs iterative
counterfactualreasoningtoprogressivelyexplore
F.Answerofourmethods
andinfereventvalues,ultimatelydeterminingthe
Here,weprovideacomparativeanalysisbetween targetoutcome. Moreover,throughintegratedeval-
our CoIn method, CausalCoT and the standard uation and backtracking mechanisms, the frame-
approach. The results are shown in Figure 9, work enables models to systematically optimize
Figure 11 and Figure 12. In results, our CoIn theirreasoningpathsandimprovereasoningaccu-
method introduces a structured, step-by-step rea- racy. Thisprocessfollowsanalgorithmicstrategy
soning framework that systematically addresses designedtosystematicallydeterminethecounter-
| complex | counterfactual |     | scenarios. | As illustrated |     | factualoutcome. |     |     |
| ------- | -------------- | --- | ---------- | -------------- | --- | --------------- | --- | --- |

|     |     |     |     |     | Solver |     |     |     |     |     | Ours |     |
| --- | --- | --- | --- | --- | ------ | --- | --- | --- | --- | --- | ---- | --- |
Models Basic Cond. Joint Nested Back. Avg. Basic Cond. Joint Nested Back. Avg.
GPT-3(Davinci-002) 50.4 50.0 50.4 50.0 49.5 50.1 51.2 48.4 48 51.6 48.5 49.6
GPT-3 (Babbage- 44.8 48.8 48.4 48.0 50.0 47.9 45.2 46.4 46 45.6 46.0 45.8
002)
GPT-3.5turbo 50.0 50.0 50.0 50.0 47.5 49.6 65.2 54.0 61.2 63.2 49.0 58.9
GPT-4omini 35.2 54.4 50.4 50.0 45.5 47.2 82.8 79.2 80.0 80.4 76.5 79.9
GPT-4o 45.6 60.8 51.6 50.4 48.0 51.4 100.0 89.6 90.0 88.4 76.5 89.4
Claude-3(Sonnet) 55.6 58.0 43.6 50.4 51.5 51.8 97.6 84.8 90.0 94.0 80.5 89.8
Claude-3.5(Haiku) 49.2 49.2 48.8 49.6 43.5 48.3 88.0 76.8 81.2 83.2 63.0 79.1
Gemini-1.5-flash 54.8 58.8 50.8 50.8 48.0 52.8 98.4 89.6 90.0 94.0 74.5 89.9
Gemini-1.5-flash-8b 52.4 50.8 49.2 51.2 47.0 50.3 94.8 80.0 88.0 88.4 64.5 83.9
Deepseek-V3 51.2 48.0 48.4 50.4 48.0 49.3 99.6 90.0 90.4 94.0 83.0 91.8
Table5: PerformanceofSolversandOurCoInAcrossDifferentReasoningCategories
Algorithm1ForwardInferenceAlgorithm anerroranalysis,categorizingtheerrorsintothree
|     |     |     |     |     |     |     | distincttypes: | BlankResponse: |     |     | Thisoccurswhen |     |
| --- | --- | --- | --- | --- | --- | --- | -------------- | -------------- | --- | --- | -------------- | --- |
Input:
|     | R:  |     |     |     |     |     | the model | produces | an  | empty | response. | Repeat- |
| --- | --- | --- | --- | --- | --- | --- | --------- | -------- | --- | ----- | --------- | ------- |
1: Asetofcausalgraphrelations
E: Asetofevents ing Error: This occurs when the model’s infer-
2:
|     | N:  |     |     |     |     |     | enceisonlyrepeatingthequestionsandgivenin- |     |     |     |     |     |
| --- | --- | --- | --- | --- | --- | --- | ------------------------------------------ | --- | --- | --- | --- | --- |
3: Asetof{event,value}pairs
|     |     |     |     |     |     |     | formations. | The | example | is  | shown | in Figure 13. |
| --- | --- | --- | --- | --- | --- | --- | ----------- | --- | ------- | --- | ----- | ------------- |
Output:
Y: targeteventY Type Mismatch: It represents that the answer is
4:
5: procedure REASONING(R,E,N) expectedtobeabinaryvalue“yes”or“no”. The
|     |        |               |            | E\N.events |     |     | responsereturnsalistwithmultiple“yes”or“no”. |     |     |     |     |     |
| --- | ------ | ------------- | ---------- | ---------- | --- | --- | -------------------------------------------- | --- | --- | --- | --- | --- |
| 6:  | K      | ← RANDOM(E),E |            | ∈          |     |     |                                              |     |     |     |     |     |
|     | whileK | ∈/            | N.eventsdo |            |     |     | TheexampleisshowninFigure14.                 |     |     |     |     |     |
7:
|     |     | forallrelationr |     | ∈ Rdo |     |     |     |     |     |     |     |     |
| --- | --- | --------------- | --- | ----- | --- | --- | --- | --- | --- | --- | --- | --- |
8:
INFER(r,N)
| 9:  |     | if  | ∃   |     | → value(K) |     |     |     |     |     |     |     |
| --- | --- | --- | --- | --- | ---------- | --- | --- | --- | --- | --- | --- | --- |
1.20
then
|     |     |     | N ← N | ∪{K,value(K)} |     |     |      |     |     |     |     |     |
| --- | --- | --- | ----- | ------------- | --- | --- | ---- | --- | --- | --- | --- | --- |
| 10: |     |     |       |               |     |     | 1.00 |     |     |     |     |     |
0.18
| 11: |            |     | ifK = Y        | then        |     |     |      |      |      | 0.19 |      |      |
| --- | ---------- | --- | -------------- | ----------- | --- | --- | ---- | ---- | ---- | ---- | ---- | ---- |
|     |            |     |                |             |     |     | 0.80 |      |      |      |      | 0.32 |
|     |            |     |                |             |     |     |      | 0.10 | 0.46 | 0.12 | 0.43 |      |
| 12: |            |     | returnvalue(K) |             |     |     |      |      |      |      |      |      |
|     |            |     | else           |             |     |     | 0.60 |      |      |      |      |      |
| 13: |            |     |                |             |     |     |      |      |      |      |      | 0.24 |
| 14: |            |     | K ←            | RANDOM(E),E |     | ∈   |      |      |      |      |      |      |
|     |            |     |                |             |     |     | 0.40 |      | 0.30 |      |      |      |
|     | E\N.events |     |                |             |     |     |      | 0.72 |      | 0.69 | 0.42 |      |
|     |            |     |                |             |     |     | 0.20 |      |      |      |      | 0.45 |
| 15: |            |     | endif          |             |     |     |      |      | 0.24 |      |      |      |
0.14
|     |     | endif  |     |     |     |     | 0.00 |                |       |                 |               |      |
| --- | --- | ------ | --- | --- | --- | --- | ---- | -------------- | ----- | --------------- | ------------- | ---- |
| 16: |     |        |     |     |     |     |      | Basic          | Cond. | Joint           | Nested        | Avg. |
| 17: |     | endfor |     |     |     |     |      | Blank Response |       | Repeating Error | Type Mismatch |      |
18: endwhile
endprocedure
| 19: |     |     |     |     |     |     | Figure10: | ErrorAnalysisforBabbage-002inCausal- |     |     |     |     |
| --- | --- | --- | --- | --- | --- | --- | --------- | ------------------------------------ | --- | --- | --- | --- |
CoT
| H.BenchmarkResultAnalysis: |     |     |     | CausalCoT |     |     |     |     |     |     |     |     |
| -------------------------- | --- | --- | --- | --------- | --- | --- | --- | --- | --- | --- | --- | --- |
WecomparedtheresponsesgeneratedbyBabbage-
| 002            | under | the CausalCoT |                               | framework | with | those |     |     |     |     |     |     |
| -------------- | ----- | ------------- | ----------------------------- | --------- | ---- | ----- | --- | --- | --- | --- | --- | --- |
| fromotherLLMs. |       |               | Theresultsrevealthatthemajor- |           |      |       |     |     |     |     |     |     |
ityofBabbage-002’sresponseswerenonsensical
whenfollowingtheCausalCoTinstructions,result-
| ing      | in a remarkably |          | low accuracy |            | of just | 8.0%.   |     |     |     |     |     |     |
| -------- | --------------- | -------- | ------------ | ---------- | ------- | ------- | --- | --- | --- | --- | --- | --- |
| A deeper |                 | analysis | showed       | that 82.4% | of      | the re- |     |     |     |     |     |     |
sponseswereclassifiedasincomprehensible,which
explainswhytheaccuracywasnotablylowerthan
| random | guessing. |     | The following |     | chart provides |     |     |     |     |     |     |     |
| ------ | --------- | --- | ------------- | --- | -------------- | --- | --- | --- | --- | --- | --- | --- |

Question:
—————-
User: Imagineaself-contained,hypotheticalworldwithonlythefollowingconditions,andwithout
any unmentioned factors or causal relationships: Pexu has a direct effect on Kraz. Not Kraz and
Pexuhasadirecteffectonhwax. Hwaxhasadirecteffectonrukz. Krazisunobserved. Weknow
thatpexuandnotkrazcauseshwax. pexucauseskraz. hwaxcausesrukz. Weobservedanindividual
ishwax. Wouldanindividualisrukzifnotkrazinsteadofkraz? Pleasefollowtheinstructionsstep
bystep. Step1. Extractthecausalgraph: Identifythecausalgraphthatdepictstherelationshipsin
thescenario. LetX=kraz;V2=pexu;V3=hwax;Y=rukz. Thediagramshouldsimplyconsistof
edgesdenotedin"var1→var2"format,separatedbycommas. IfyougetV1→NotV2forexample,
youneedtoreplaceintoV1→V2. Step2. AbductionandActionforinformationcollection: Collect
all the directly given information into given values set. 1 means given observed in question or
observed. 0meansgivennotinquestion. Donotassumeorinferothervariablesvaluesbyrelations.
Then, describe relations about how multiple variables influence another variable; it can result in
AND,OR,orNOT.Step3. InferandPredicttheYbyinformationstepbystep. Step4. Basedonthe
resultfromtheStep3,derivethefinalanswer. Thereisanidentifiableanswer.
Assistant:
Step 1) Extract the causal graph: Identify the causal graph that depicts the relationships in the
scenario. LetV2=kraz; X=pexu; V3=hwax; Y=rukz. ThecausalgraphisV2→V3, V2→X,
X→V3,V3→Y.
Step2)AbductionandActionforinformationcollection: Allgivenvalues: V2=1,andX=0(by
abduction,V2occurs),X=0(byaction,Xnotoccur);Relations: Y:(NOTV2)ANDV3,V3: X
ANDNOTV2.
Step3)Tryingapromisingfirstoperation:
1. V3=notXandV2=1
-Y=V3=1→foundit!
Backtrackingthesolution:
Step3a:
V3=notXandV2=1
Step3b:
Y=V3=1
Step4)SincetheresultfortheYis1,theoverallanswertothequestionisyes.
—————-
User: Imagineaself-contained,hypotheticalworldwithonlythefollowingconditions,andwithout
anyunmentionedfactorsorcausalrelationships: VankhasadirecteffectonPraf,Prafhasadirect
effect on Scud, Scud has a direct effect on Wrenk, Wrenk and Scud have direct effects on Yobb,
YobbhasadirecteffectonGlim,GlimandScudhavedirecteffectsonSpog,andSpoghasadirect
effectonKlep. VankBern(0.6). WeobservedWrenk. WeknowthatVankcausesPraf,Prafcauses
Scud,ScudcausesWrenk,WrenkandScudtogethercauseYobb,YobbcausesGlim,GlimandScud
together cause Spog, and Spog causes Klep. Vank Bern(0.6). We observed Wrenk. Would Klep
occur ifnot Prafinstead of Praf? Step 1. Extract thecausal graph: Identifythe causalgraph that
depictstherelationshipsinthescenario. LetX=Ziklo;V1=Blaf;V2=Trune;V3=Vork;V4=
Sline;V5=Frim;V6=Qado;Y=Lumbo. Thediagramshouldsimplyconsistofedgesdenoted
in"var1→var2"format, separatedbycommas. IfyougetV1→NotV2forexample, youneed
toreplaceintoV1→V2. Step2. AbductionandActionforinformationcollection: Collectallthe
directlygiveninformationintogivenvaluesset. 1meansgivenobservedinquestionorobserved.
0 means given not in question. Do not assume or infer other variables values by relations. Then,
describerelationsabouthowmultiplevariablesinfluenceanothervariable;itcanresultinAND,OR,
orNOT.Step3. InferandPredicttheYbyinformationstepbystep. Step4. Basedontheresultfrom
theStep3,derivethefinalanswer. Thereisanidentifiableanswer.
Assistant:
Figure5: ThepromptdesignexampleofCoIn

100%
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10%
0%
|           | Wrong Relations | Wrong Inference |      | Wrong Conclusion |     |     |     |     |     |     |
| --------- | --------------- | --------------- | ---- | ---------------- | --- | --- | --- | --- | --- | --- |
|           |                 | CausalCoT       | Ours |                  |     |     |     |     |     |     |
| Figure 6: | Error Analysis  | comparison      |      | between Our      |     |     |     |     |     |     |
MethodandCausalCoT.
|     |     |     |     |     | Question: | Imagine |     | a self-contained, |     | hy- |
| --- | --- | --- | --- | --- | --------- | ------- | --- | ----------------- | --- | --- |
Question: Imagineaself-contained,hypothet- pothetical world with only the following
icalworldwithonlythefollowingconditions,
|     |     |     |     |     | conditions, | and | without | any | unmentioned |     |
| --- | --- | --- | --- | --- | ----------- | --- | ------- | --- | ----------- | --- |
andwithoutanyunmentionedfactorsorcausal
|     |     |     |     |     | factors | or causal | relationships: |     | Nuv | has a |
| --- | --- | --- | --- | --- | ------- | --------- | -------------- | --- | --- | ----- |
relationships: Having a brother has a direct direct effect on Splee, Blen and Druk, not
| effectonroom. |                             | Thecandlehasadirecteffect |     |     |               |          |        |          |         |       |
| ------------- | --------------------------- | ------------------------- | --- | --- | ------------- | -------- | ------ | -------- | ------- | ----- |
|               |                             |                           |     |     | Druk has      | a direct | effect | on Plog, | Plog    | has a |
| onroom.       | Weknowthathavingabrotherand |                           |     |     |               |          |        |          |         |       |
|               |                             |                           |     |     | direct effect | on       | Skrim, | Skrim    | or Druk | has   |
candle with wax causes dark room. We ob- a direct effect on Zimb, Zimb has a direct
servedthecandlehaswax. Wouldtheroomis effectonYurd,andYurdhasadirecteffecton
darkifnothavingabrotherinsteadofhaving
Wrox. WeknowthatNuvcausesSplee,Blen
abrother?
andDruk,notDrukcausesPlog,Plogcauses
Start your answer with “Yes” or “No”, fol- Skrim, Skrim or Druk causes Zimb, Zimb
lowedbyadditionalreasoningorevidenceto
|     |     |     |     |     | causesYurd,andYurdcausesWrox. |     |     |     |     | Would |
| --- | --- | --- | --- | --- | ----------------------------- | --- | --- | --- | --- | ----- |
supportyourexplanation.
WroxoccurifnotNuvandnotSplee?
|           |                         |     |                 |       | Answer:  | No.                        |     |     |     |     |
| --------- | ----------------------- | --- | --------------- | ----- | -------- | -------------------------- | --- | --- | --- | --- |
| Figure7:  | Anti-commonsenseExample |     |                 |       |          |                            |     |     |     |     |
|           |                         |     |                 |       | Figure9: | StandardInstructionExample |     |     |     |     |
| Question: | Imagine                 | a   | self-contained, | hypo- |          |                            |     |     |     |     |
theticalworldwithonlythefollowingcondi-
| tions, and              | without                    | any               | unmentioned     | factors    |     |     |     |     |     |     |
| ----------------------- | -------------------------- | ----------------- | --------------- | ---------- | --- | --- | --- | --- | --- | --- |
| orcausalrelationships:  |                            |                   | Themanintheroom |            |     |     |     |     |     |     |
| hasadirecteffectonroom. |                            |                   | Thecandlehasa   |            |     |     |     |     |     |     |
| directeffectonroom.     |                            | Weknowthatblowing |                 |            |     |     |     |     |     |     |
| out the                 | candle                     | and candle        | with            | wax causes |     |     |     |     |     |     |
| darkroom.               | Weobservedthecandlehaswax. |                   |                 |            |     |     |     |     |     |     |
Wouldtheroomisdarkifnotblowingoutthe
candleinsteadofblowingoutthecandle?
| Start your | answer | with | “Yes” | or “No”, fol- |     |     |     |     |     |     |
| ---------- | ------ | ---- | ----- | ------------- | --- | --- | --- | --- | --- | --- |
lowedbyadditionalreasoningorevidenceto
supportyourexplanation.
Figure8: CommonsenseExample

Question: Imagine a self-contained, hypothetical world with only the following conditions, and
withoutanyunmentionedfactorsorcausalrelationships: NuvhasadirecteffectonSplee,Blenand
Druk,notDrukhasadirecteffectonPlog,PloghasadirecteffectonSkrim,SkrimorDrukhasa
directeffectonZimb,ZimbhasadirecteffectonYurd,andYurdhasadirecteffectonWrox. We
knowthatNuvcausesSplee,BlenandDruk,notDrukcausesPlog,PlogcausesSkrim,SkrimorDruk
causesZimb,ZimbcausesYurd,andYurdcausesWrox. WouldWroxoccurifnotNuvandnotSplee?
Answer: Toaddresstheproblem,wewillfollowthestepsoutlined:
Step1: Extractthecausalgraph
Basedonthegivenconditions,thecausalgraphcanberepresentedasfollows:
-Nuv→Splee-Nuv→Blen-Nuv→Druk-Druk→Plog-Plog→Skrim-Skrim→Zimb-Druk
→Zimb-Zimb→Yurd-Yurd→Wrox
Step2: Determinethequerytype
The question asks whether Wrox would occur if not Nuv and not Splee. This is a counterfactual
query because it involves reasoning about what would happen under a hypothetical scenario that
differsfromtheobservedworld.
Thequerytypeis: “counterfactual”
Step3: Formalizethequery
Theformalexpressionforthecounterfactualqueryis:
Wrox
Nuv=0,Splee=0
ThisnotationrepresentsthevalueofWroxinthecounterfactualworldwhereNuvandSpleedonot
occur.
Step4: Gatherallrelevantdata
Fromtheproblemstatement,wehavethefollowingdata:
-Nuv=0(notNuv)-Splee=0(notSplee)
Step5: Deducetheestimandusingcausalinference
Todeducetheestimand,weneedtoconsiderthecausalpathwaysfromNuvandSpleetoWrox:
1. Nuv directly affects Splee, Blen, and Druk. 2. Druk affects Plog, which affects Skrim, which
affectsZimb,whichaffectsYurd,whichaffectsWrox. 3. DrukalsodirectlyaffectsZimb. 4. Zimb
affectsYurd,whichaffectsWrox.
GiventhatNuv=0,Splee=0,weneedtodetermineifWroxcanstilloccur:
-SinceNuv=0,Splee=0,Blen=0,andDruk=0. -Druk=0impliesPlog=0andZimb=0(since
DrukaffectsbothPlogandZimb). -Plog=0impliesSkrim=0. -Skrim=0andDruk=0imply
Zimb=0. -Zimb=0impliesYurd=0. -Yurd=0impliesWrox=0.
Thus,thecounterfactualscenarioresultsinWrox=0.
Step6: Calculatetheestimand
Giventhedeductionsabove,thecounterfactualvalueofWroxwhenNuv=0andSplee=0is:
Wrox = 0
Nuv=0,Splee=0
Therefore,WroxwouldnotoccurifnotNuvandnotSplee.
Figure11: CausalCoTInstructionExample

Question: Imagine a self-contained, hypothetical world with only the following conditions, and
withoutanyunmentionedfactorsorcausalrelationships: NuvhasadirecteffectonSplee,Blenand
Druk,notDrukhasadirecteffectonPlog,PloghasadirecteffectonSkrim,SkrimorDrukhasa
directeffectonZimb,ZimbhasadirecteffectonYurd,andYurdhasadirecteffectonWrox. We
knowthatNuvcausesSplee,BlenandDruk,notDrukcausesPlog,PlogcausesSkrim,SkrimorDruk
causesZimb,ZimbcausesYurd,andYurdcausesWrox. WouldWroxoccurifnotNuvandnotSplee?
Answer: Step1)Extractthecausalgraph: Identifythecausalgraphthatdepictstherelationshipsin
thescenario. LetX=Nuv;V1=Splee;V2=Blen;V3=Druk;V4=Plog;V5=Skrim;V6=Zimb;
V7=Yurd;Y=Wrox. Thecausalgraphis:
X→V1,X→V2,X→V3,V3→V4,V4→V5,V5→V6,V3→V6,V6→V7,V7→Y.
Step2)AbductionandActionforinformationcollection: Allgivenvalues: X=0(notNuv),V1=0
(notSplee). Relations:
-V1: X
-V2: X
-V3: X
-V4: NOTV3
-V5: V4
-V6: V5ORV3
-V7: V6
-Y:V7
Step3)Adoptthefollowingalgorithmtogettheresult: InfertheYbyinformationstepbystep.
1. V1=X=0
2. V2=X=0
3. V3=X=0
4. V4=NOTV3=1
5. V5=V4=1
6. V6=V5ORV3=1OR0=1
7. V7=V6=1
8. Y=V7=1
Step 4) Conclude the final answer: Since the result for Y (Wrox) is 1, the overall answer to the
questionisyes. WroxwouldoccurifnotNuvandnotSplee.
Figure12: CoInInstructionExample

Response
GlentcausesRazz,RazzandGlenttogethercausePex,PexcausesZurn,ZurncausesMelf,andMelf
andRazztogethercauseZlim. WouldZlimoccurifnotGlentinsteadofGlent?
B:GlentcausesRazz,RazzandGlenttogethercausePex,PexcausesZurn,ZurncausesMelf,and
MelfandRazztogethercauseZlim. WouldZlimoccurifnotGlentinsteadofGlent?
C:GlentcausesRazz,RazzandGlenttogethercausePex,PexcausesZurn,ZurncausesMelf,and
MelfandRazztogethercauseZlim. WouldZlimoccurifnotGlentinsteadofGlent?
D:GlentcausesRazz,RazzandGlenttogethercausePex,PexcausesZurn,ZurncausesMelf,and
MelfandRazztogethercauseZlim. WouldZlimoccurifnotGlentinsteadofGlent?
E:GlentcausesRazz,RazzandGlenttogethercausePex,PexcausesZurn,ZurncausesMelf,and
MelfandRazztogethercauseZlim. WouldZlimoccurifnotGlentinsteadofGlent?
F:GlentcausesRazz,RazzandGlenttogethercausePex,PexcausesZurn,ZurncausesMelf,and
MelfandRazztogethercauseZlim. WouldZlimoccurifnotGlentinsteadofGlent?
G:GlentcausesRazz,RazzandGlenttogethercausePex,PexcausesZurn,ZurncausesMelf,and
MelfandRazztogethercauseZlim. WouldZlimoccurifnotGlentinsteadofGlent?
H:GlentcausesRazz,RazzandGlenttogethercausePex,PexcausesZurn,ZurncausesMelf,and
MelfandRazztogethercauseZlim. WouldZlimoccurifnotGlentinsteadofGlent?
I:GlentcausesRazz,RazzandGlenttogethercausePex,PexcausesZurn,ZurncausesMelf,and
MelfandRazztogethercauseZlim. WouldZlimoccurifnotGlentinsteadofGlent?
Figure13: ConclusionErrorExample
Response
Thecorrectansweris(0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
Figure14: TypeMismatch