Datasets:

luoojason
/

muddle-eval-bundle-md

		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

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
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terfactualreasoningcapabilitiesofLLMs. model. arXivpreprintarXiv:2408.06849.
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					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:

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% 90% 80% 70% 60% 50% 40% 30% 20% 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:

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

V1=X=0
V2=X=0
V3=X=0
V4=NOTV3=1
V5=V4=1
V6=V5ORV3=1OR0=1
V7=V6=1
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