| { |
| "paper_id": "2020", |
| "header": { |
| "generated_with": "S2ORC 1.0.0", |
| "date_generated": "2023-01-19T08:12:20.915366Z" |
| }, |
| "title": "Linguistic interpretation as inference under argument system uncertainty: the case of epistemic must", |
| "authors": [ |
| { |
| "first": "Brandon", |
| "middle": [], |
| "last": "Waldon", |
| "suffix": "", |
| "affiliation": { |
| "laboratory": "", |
| "institution": "Stanford University", |
| "location": { |
| "addrLine": "450 Jane Stanford Way Stanford", |
| "postCode": "94305", |
| "region": "CA", |
| "country": "USA" |
| } |
| }, |
| "email": "bwaldon@stanford.edu" |
| } |
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| "year": "", |
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| "identifiers": {}, |
| "abstract": "Modern semantic analyses of epistemic language (incl. the modal must) can be characterized by the 'credence assumption': speakers have full certainty regarding the propositions that structure their epistemic states. Intuitively, however: a) speakers have graded, rather than categorical, commitment to these propositions, which are often never fully and explicitly articulated; b) listeners have higherorder uncertainty about this speaker uncertainty; c) must \u03c6 is used to communicate speaker commitment to some conclusion \u03c6 and to indicate speaker commitment to the premises that condition the conclusion. I explore the consequences of relaxing the credence assumption by extending the argument system semantic framework first proposed by Stone (1994) to a Bayesian probabilistic framework of modeling pragmatic interpretation (Goodman and Frank, 2016). 1", |
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| "paper_id": "2020", |
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| "abstract": [ |
| { |
| "text": "Modern semantic analyses of epistemic language (incl. the modal must) can be characterized by the 'credence assumption': speakers have full certainty regarding the propositions that structure their epistemic states. Intuitively, however: a) speakers have graded, rather than categorical, commitment to these propositions, which are often never fully and explicitly articulated; b) listeners have higherorder uncertainty about this speaker uncertainty; c) must \u03c6 is used to communicate speaker commitment to some conclusion \u03c6 and to indicate speaker commitment to the premises that condition the conclusion. I explore the consequences of relaxing the credence assumption by extending the argument system semantic framework first proposed by Stone (1994) to a Bayesian probabilistic framework of modeling pragmatic interpretation (Goodman and Frank, 2016). 1", |
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| "section": "Abstract", |
| "sec_num": null |
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| "body_text": [ |
| { |
| "text": "Natural language contains a variety of means for expressing one's epistemic state. The best-studied of these in the semantics literature are the epistemic modal auxiliaries must and may/might:", |
| "cite_spans": [], |
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| "section": "Introduction", |
| "sec_num": "1" |
| }, |
| { |
| "text": "(1) a. Ann: Where is Peter? b. Mary: He {may/might/must} be in his office.", |
| "cite_spans": [], |
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| "section": "Introduction", |
| "sec_num": "1" |
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| "text": "There is broad agreement in the literature that Mary's response in (1b) is comprised in part by a conclusion -Peter is in his office -the 'prejacent' over which the modal takes semantic scope. Additionally, the consensus is that the epistemic modal expresses a connection between the prejacent and a set of salient premises -most commonly, things that are known and/or assumed by the speaker and/or her interlocutor. Roberts (2019) 1 I gratefully acknowledge Cleo Condoravdi, Judith Degen, Atticus Geiger, Daniel Lassiter, Christopher Potts, three PaM reviewers, and Stanford's Construction of Meaning workshop for valuable feedback. All errors are mine.", |
| "cite_spans": [ |
| { |
| "start": 417, |
| "end": 431, |
| "text": "Roberts (2019)", |
| "ref_id": "BIBREF7" |
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| "text": "notes that the details beyond these points of agreement are matters of debate; in particular, theoreticians disagree over the following two questions:", |
| "cite_spans": [], |
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| "section": "Introduction", |
| "sec_num": "1" |
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| { |
| "text": "1. How do we specify the premises -the body of information, assumptions, or other contextually-supplied propositions which condition a modalized statement?", |
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| "ref_spans": [], |
| "eq_spans": [], |
| "section": "Introduction", |
| "sec_num": "1" |
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| { |
| "text": "2. In what way are the premises related to the conclusion \u03c6 encoded as the prejacent of a modalized statement?", |
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| "sec_num": "1" |
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| "text": "A well-discussed desideratum of a successful theory of epistemic modality is that it should provide an understanding of the perceived weakness of must. An observation going back to Karttunen (1972) is that modalized statements of the form must \u03c6 appear to mark weak speaker commitment to the prejacent compared to the unmodalized counterpart, 'bare' \u03c6. The observation stems from consideration of contexts such as (2):", |
| "cite_spans": [ |
| { |
| "start": 181, |
| "end": 197, |
| "text": "Karttunen (1972)", |
| "ref_id": "BIBREF3" |
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| "text": "(2) (In the context of direct observation of rain): a. # It must be raining outside. b. It is raining outside.", |
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| "text": "Answers to Roberts' original questions fall into three categories. Restricted quantificational accounts (Kratzer, 1991) posit that the set of premises includes propositions known to a contextually-salient individual (most often the speaker) or group of individuals (containing the speaker and her interlocutor), as well as a contextually-specified set of assumptions which further restrict the space of epistemic possibilities. Must/might \u03c6 quantify universally and existentially over this space, respectively: must expresses that the conclusion is true at all possible worlds where the known and assumed propositions are true; might expresses that the conclu-sion is true at at least one of those worlds. Perceived weakness of must is accounted for on this analysis because must \u03c6 -unlike bare \u03c6 -allows for the possibility that \u00ac\u03c6 is true in worlds compatible with the known propositions (but incompatible with the assumed ones). In contrast, unrestricted quantificational accounts (von Fintel and Gillies, 2010) posit that must quantifies over a space of epistemic possibilities that is unconstrained by contextually-salient assumptions. On this approach, must \u03c6 is incompatible with \u00ac\u03c6, and must's infelicity in (2) is a consequence of a violation of independently-stipulated felicity conditions. 2 Finally, probabilistic accounts (Swanson, 2006; Lassiter, 2016) vary in their commitments regarding how to specify the premises but consider must/might to be operators which take as their input the premises and output a statement about the likelihood of the truth of the prejacent.", |
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| { |
| "start": 104, |
| "end": 119, |
| "text": "(Kratzer, 1991)", |
| "ref_id": "BIBREF4" |
| }, |
| { |
| "start": 984, |
| "end": 1014, |
| "text": "(von Fintel and Gillies, 2010)", |
| "ref_id": "BIBREF0" |
| }, |
| { |
| "start": 1335, |
| "end": 1350, |
| "text": "(Swanson, 2006;", |
| "ref_id": "BIBREF10" |
| }, |
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| "start": 1351, |
| "end": 1366, |
| "text": "Lassiter, 2016)", |
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| "text": "All of the above approaches can be characterized by what I call the credence assumption -that is, that however we specify the premises and their relation to the conclusion, speakers have full certainty about the premises upon which they can rely for the purposes of inference in a given context. This assumption is desirable from the standpoint of analytic simplicity; moreover, it provides a way of analyzing modal disagreement, as in (3):", |
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| "text": "(3) a. Ann: It might be raining outside. b. Mary: No, it cannot be raining outside! On the credence assumption, Ann makes a statement regarding the possibility of rain given a set of known and/or assumed propositions. Mary assesses this statement and disagrees: she has a different (yet also deterministic) understanding of the premises operable in this discourse. 3 Intuitively, however, speakers' epistemic states are much more complex than the credence assumption allows. Namely, these states involve graded, rather than deterministic, commitments to propositions that are often never fully and explicitly articulated by speakers who produce statements of the form must/might \u03c6. Listeners in turn have uncertainty about the premises which their interlocutors deem to be relevant for the purposes of inference and deliberation; indeed, must/might \u03c6 is informative not just because it conveys speaker's epistemic commitment to the prejacent but also because it conveys something about the speaker's underlying knowledge and assumptions about the world, and about how she is likely to use available information in the future.", |
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| "start": 365, |
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| "text": "3", |
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| "text": "I develop a quantitative framework of modeling interpretation of must that relaxes the credence assumption. In doing so, I offer a formal means of representing how these constructions can be informative with respect to speaker commitment to the conclusion as well as with respect to the premises that the speaker believes are operable in context. My point of departure is the argument system semantic framework of Stone (1994) , followed by a probabilistic enrichment of that framework rooted in a Bayesian understanding of linguistic inference (Goodman and Frank, 2016). On this approach, communication proceeds between agents who are uncertain about what premises can (and should) be relied upon for the purposes of present and future inference and deliberation. Interlocutors align this uncertainty in part via communicative exchange. Finally, I consider implications of this approach for our understanding of conversational dynamics and the common ground.", |
| "cite_spans": [ |
| { |
| "start": 414, |
| "end": 426, |
| "text": "Stone (1994)", |
| "ref_id": "BIBREF9" |
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| "text": "2 Argument system semantics Stone (1994) observes that in contexts such as (1), the must-variant of Mary's response is infelicitous if the context does not make clear (to Ann) the basis on which Mary's conclusion is made: Mary's conclusion about Peter may come from the fact that Mary has ruled out all possible other places Peter could be, or perhaps it is 3pm on a Tuesday and Peter is always in his office at that time. If Ann cannot recover Mary's argument in support of the conclusion, then must is infelicitous in (1). On Stone (1994) 's semantics, must \u03c6 is true iff a (possibly defeasible) argument A -made somehow salient in the context -justifies concluding \u03c6 given an argument system K. I recapitulate the relevant details of Stone's analysis below. 4", |
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| "start": 28, |
| "end": 40, |
| "text": "Stone (1994)", |
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| "start": 528, |
| "end": 540, |
| "text": "Stone (1994)", |
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| "sec_num": "1" |
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| { |
| "text": "Let K be an argument system, comprised of a set of established propositions K (ground formulae K C and logical rules of inference K N ) and a set of defeasible inferential rules \u2206. Arguments for ground formulae are defined as follows: 5", |
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| "section": "Formal preliminaries", |
| "sec_num": "2.1" |
| }, |
| { |
| "text": "Definition 1:", |
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| "section": "Formal preliminaries", |
| "sec_num": "2.1" |
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| "text": "A set T of instantiations of elements of \u2206 is an ARGUMENT for h ( T, h K ) iff: (1) K \u222a T h; (2) K \u222a T \u22a5; and (3) for no T \u2282 T, K \u222a T h.", |
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| "sec_num": "2.1" |
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| "text": "The first clause of Definition 1 specifies that an argument for a ground formula (comprised of elements of \u2206), added to K, entails the formula; the second specifies that the argument must be consistent with K; the third specifies that the argument must be minimal. Stone also introduces the notion of a sub-argument: an argument which can be computed from the premises of another argument:", |
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| "section": "Formal preliminaries", |
| "sec_num": "2.1" |
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| "text": "Definition 2: S, j K is a SUBARGUMENT of T, h K if and only if S \u2286 T .", |
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| "section": "Formal preliminaries", |
| "sec_num": "2.1" |
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| "text": "Stone emphasizes that subarguments of T, h K need not play a role in concluding h. Rather, the set of subarguments for h include all arguments which can be generated from T given argument system K. This means that counterarguments to T, h K can do so by targeting not only subarguments necessary to conclude h from T but any inference generated from T given K.", |
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| "sec_num": "2.1" |
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| "text": "Definition 3: T 1 , h 1 K COUNTERARGUES T 2 , h 2 K at T, h K if and only if T, h K is a subargument of T 2 , h 2 K and K \u222a {h, h 1 } \u22a5.", |
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| "section": "Formal preliminaries", |
| "sec_num": "2.1" |
| }, |
| { |
| "text": "A counterargument defeats an argument if the former is more specific -if it \"takes more particulars of the context into consideration\" (1994: 6).", |
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| "section": "Formal preliminaries", |
| "sec_num": "2.1" |
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| "text": "Definition 4: T 1 , h 1 K is more SPECIFIC than T 2 , h 2 K if and only if:", |
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| "text": "(1) for all ground formu- lae e, if K N \u222a {e} \u222a T 1 h 1 but K N \u222a {e} h 1 , then K N \u222a {e} \u222a T 2 h 2 ; and (2) there is some ground e such that K N \u222a {e} \u222a T 2 h 2 , K N \u222a {e} \u222a T 1 h 1 , and K N \u222a {e} h 2 . Definition 5: T 1 , h 1 K DEFEATS T 2 , h 2 K if T 1 , h 1 K counterargues T 2 , h 2 K at T, h K and T 1 , h 1 K is more specific than T, h K", |
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| "section": "Formal preliminaries", |
| "sec_num": "2.1" |
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| "text": "The first clause of Definition 4 states that the conclusion of the less specific argument h 2 must be entailed by the argument system coupled with the argument's defeasible premises T 2 , provided the argument system is one in which the more specific argument's conclusion h 1 only follows with the addition of its premises T 1 . The second clause states that there must be some argument system 5 All definitions below can be found in Stone (1994) : p. 6. which entails the conclusion of the less specific argument h 2 on the basis of the premises T 2 but is inconsistent with the conclusion of the more specific argument h 1 on the basis of premises T 1 .", |
| "cite_spans": [ |
| { |
| "start": 435, |
| "end": 447, |
| "text": "Stone (1994)", |
| "ref_id": "BIBREF9" |
| } |
| ], |
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| "section": "Formal preliminaries", |
| "sec_num": "2.1" |
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| "text": "An argument system justifies an argument \"whenever [the argument] has no counterarguments which are not themselves defeated\" (1994: 6). To formalize this, Stone introduces the concepts of supporting arguments and interfering arguments, defined inductively to capture the fact that for an argument to be justified it must not be defeated at any level of sub-argumentation.", |
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| "section": "Formal preliminaries", |
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| "text": "Definition 6: All arguments are level 0 supporting and interfering arguments.", |
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| "sec_num": "2.1" |
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| "text": "\u2022 An argument T 1 , h 1 K is a level (n + 1) supporting argument if and only if no level n interfering argument counters it at any of its subarguments.", |
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| "eq_spans": [], |
| "section": "Formal preliminaries", |
| "sec_num": "2.1" |
| }, |
| { |
| "text": "\u2022 An argument T 1 , h 1 K is a level (n + 1) in-", |
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| "ref_spans": [], |
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| "section": "Formal preliminaries", |
| "sec_num": "2.1" |
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| { |
| "text": "terfering argument if there is no level n interfering argument which defeats it.", |
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| "ref_spans": [], |
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| "section": "Formal preliminaries", |
| "sec_num": "2.1" |
| }, |
| { |
| "text": "Definition 7: An argument T, h K JUSTIFIES h in K if and only if there is some m such that for all n \u2265 m, T, h K is a level n supporting argument. h is justified in K if some T, h K justifies it in K.", |
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| "section": "Formal preliminaries", |
| "sec_num": "2.1" |
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| { |
| "text": "First, let K 0 be an argument system consisting of ground formulae K 0 C , logical rules K 0 N , and defeasible rules \u2206 0 . 6 Assume K 0 N contains a forward chain inferential rule, and \u2206 0 consists of the following defeasible rules about matches and heat:", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "Illustration", |
| "sec_num": "2.2" |
| }, |
| { |
| "text": "A: match(x) \u2227 strike(x) > lit(x) B: match(x) \u2227 strike(x) \u2227 wet(x) > \u00aclit(x) C: lit(x) > hot(x)", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "Illustration", |
| "sec_num": "2.2" |
| }, |
| { |
| "text": "Let K 0 C contain two ground formulae match(m1) and strike(m1). By Definition 1, we generate two arguments, A 1 and A 2 :", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "Illustration", |
| "sec_num": "2.2" |
| }, |
| { |
| "text": "A 1 : {A}, lit(m1) K 0 A 2 : {A, C}, hot(m1) K 0", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "Illustration", |
| "sec_num": "2.2" |
| }, |
| { |
| "text": "Now, consider Stone's semantics for must:", |
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| "ref_spans": [], |
| "eq_spans": [], |
| "section": "Illustration", |
| "sec_num": "2.2" |
| }, |
| { |
| "text": "(4) Must \u03c6 is true in K iff K A, \u03c6 K", |
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| "section": "Illustration", |
| "sec_num": "2.2" |
| }, |
| { |
| "text": "That is, Must \u03c6 is true if a contextually-salient argument A justifies concluding \u03c6 in a given argument system. Given K 0 , (5) is true:", |
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| "ref_spans": [], |
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| "section": "Illustration", |
| "sec_num": "2.2" |
| }, |
| { |
| "text": "(5) The match must have lit.", |
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| "ref_spans": [], |
| "eq_spans": [], |
| "section": "Illustration", |
| "sec_num": "2.2" |
| }, |
| { |
| "text": "Note that the semantics of must requires (in the case of 5) that the argument (A 1 ) is contextuallysalient; otherwise, must is undefined. Assuming this condition is met, we can verify the truth of (5) by considering, by Definition 7, whether concluding lit(m1) from A 1 is justified in K 0 . It is: the only arguments that could interfere would have as their conclusion \u00aclit(m1), but these arguments cannot be generated from K 0 because wet(x) is not in K C 0 (and Rule B cannot be invoked).", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "Illustration", |
| "sec_num": "2.2" |
| }, |
| { |
| "text": "Now consider a second argument system K 1 , which differs minimally from K 0 in that wet(m1) is an additional ground formula. Thus, A 3 is generated in addition to A 1 and A 2 :", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "Illustration", |
| "sec_num": "2.2" |
| }, |
| { |
| "text": "A 3 : {B}, \u00aclit(m1) K 1", |
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| "ref_spans": [], |
| "eq_spans": [], |
| "section": "Illustration", |
| "sec_num": "2.2" |
| }, |
| { |
| "text": "In K 1 , (5) is false. Note first that the only argument from which lit(m1) can be concluded is A 1 . Thus, as in K 0 , (5) can only be true if A 1 is justified. It is not in K 1 : A 3 defeats A 1 because the former is more specific than the latter.", |
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| "ref_spans": [], |
| "eq_spans": [], |
| "section": "Illustration", |
| "sec_num": "2.2" |
| }, |
| { |
| "text": "Stone's system provides a straightforward account of must's perceived weakness, if we can assume that direct observation of h adds h to the set of ground formulae by default. Consider Definition 1: an argument for h in K must have as its premises the minimal set of defeasible rules of inference which -coupled with the set of established ground formulae and the logical rules of inference in K -entails h. If h is already in the set of ground formulae, then the minimal set of required premises is empty. The prediction is that there is no argument A that can meet the definedness conditions of must \u03c6 if \u03c6 is already established in K.", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "Interim discussion", |
| "sec_num": "2.3" |
| }, |
| { |
| "text": "Argument systems and speaker epistemic states are assumed to be one and the same on this analysis, meaning that this analysis can be characterized by the credence assumption. We might imagine one speaker whose epistemic state is akin to argument system K 0 , and another whose state is akin to K 1 . On this analysis, it is clear why these two agents might disagree over (5): the statement is true given the former argument system and false given the latter. Below, I explore the properties of an extension that relaxes the credence assumption.", |
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| "section": "Interim discussion", |
| "sec_num": "2.3" |
| }, |
| { |
| "text": "In the context of Stone's analysis, relaxing the credence assumption amounts to revising our as-sumptions regarding the speaker's relationship to K. I define a space of possible argument systems Z, which I allow to vary according to their ground formulae and defeasible rules of inference. I assume that speakers are uncertain as to what precise argument system is the relevant one for the purposes of inference and decision making in context. That is, there may be some uncertainty as to whether particular ground formulae can be taken to be true at the world of evaluation, or there may be uncertainty as to whether certain defeasible rules of inference may (or should) be employed in a particular context. I assume that Z is specified such that the ground formulae that the speaker considers likely to be true are in many (but not perhaps not all) of the elements of Z; the same is assumed modulo the defeasible rules of inference. 7 We can then define speaker commitment to a proposition \u03c6 on the basis of some argument A as the likelihood that A, \u03c6 justifies \u03c6 given possible argument systems in Z. Must \u03c6, then, is a comment on this likelihood value: if the likelihood exceeds a certain contextually-specified threshold, then the statement is true:", |
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| "section": "Probabilistic argument system semantics", |
| "sec_num": "3" |
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| "text": "(6) Must \u03c6 is true in Z iff P A, \u03c6 Z > \u03b8,", |
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| "ref_spans": [], |
| "eq_spans": [], |
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| "sec_num": "3" |
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| { |
| "text": "where P A, \u03c6 Z = K\u2208Z K A,\u03c6 K", |
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| "text": "Speakers produce must \u03c6 to convey their degree of belief that \u03c6 is a valid conclusion on the basis of an argument A, given their argument system uncertainty. But importantly, the precise nature of this argument system uncertainty -the precise value of Z -is not transparent to the listener: the listener has prior beliefs about possible values of Z that are updated according to the conclusions that a speaker draws (and argumentation that she employs to draw those conclusions) in a particular context. Observation of must \u03c6, then, allows the listener to update her uncertainty about the speaker's Z distribution.", |
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| "text": "The speaker's production of must \u03c6 is determined by a utility function of utterances given intended meanings that balances informativity against production cost. Following Goodman and Frank (2016) , the model of a pragmatic speaker S 1 is defined partly in reference to a literal L 0 listener whose interpretations are a function of utterances' literal truth/falsity given possible intended meanings. The space of possible meanings that the speaker could try to convey are possible valuations of the speaker's Z distribution (from which -by 6the speaker's commitment to \u03c6 can be computed).", |
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| "section": "|Z|", |
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| "text": "The literal L 0 listener, then, can be modeled as a conditional probability distribution over possible valuations of Z given observation of some utterance u and a contextually-supplied value for the probability threshold \u03b8. Following Lassiter and Goodman (2013) , who model interpretation of gradable adjectives using a threshold-based semantics, I assume that this \u03b8 variable is passed from L 0 and eventually estimated by the pragmatic L 1 listener (defined below) from a prior distribution over values of \u03b8.", |
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| "section": "|Z|", |
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| { |
| "text": "P L 0 (Z|u, \u03b8) = P L 0 (Z| u \u03b8 = 1) \u00d7 P (Z)", |
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| "section": "|Z|", |
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| "text": "The pragmatic speaker selects utterances to convey intended meanings according to their contextual informativeness for L 0 as well as the cost of utterance production. Below, \u03b1 is a speaker optimality parameter, and C is a cost function defined for all possible utterance choices: all else equal, the greater C(u), the lower the probability that S 1 selects u to convey a particular message.", |
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| "ref_spans": [], |
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| "section": "|Z|", |
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| }, |
| { |
| "text": "P S 1 (u|Z, \u03b8) \u221d exp(\u03b1\u00d7log(P L 0 (Z|u, \u03b8))\u2212C(u))", |
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| "section": "|Z|", |
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| "text": "The pragmatic listener L 1 's interpretations of utterances are a function of expected behavior of S 1 , as well as prior expectations about the likelihood of different possible meanings and prior expectations about the threshold value \u03b8:", |
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| "ref_spans": [], |
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| "section": "|Z|", |
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| { |
| "text": "P L 1 (Z, \u03b8|u) \u221d P S 1 (u|Z, \u03b8) \u00d7 P (Z, \u03b8)", |
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| "ref_spans": [], |
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| "section": "|Z|", |
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| "text": "Thus, interpretation of must is a joint inference about the state of the world (speaker beliefs regarding the justifiability of concluding \u03c6) and the value of a semantic threshold variable \u03b8. These speaker beliefs -P A, \u03c6 Z -can be computed given values the argument variable supplied categorically by the context (A) and one additional variable (Z) which is inferred under uncertainty.", |
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| "section": "|Z|", |
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| "text": "For this illustration, I assume that the listener has uniform prior beliefs over the threshold value \u03b8 and that she considers two possible utterance production choices: must -whose truth conditions are as in (6) -and a trivially true null message. 8 The listener assumes that the speaker has full certainty about the following features of the argument system: the ground formulae (consisting of propositions match(m1), strike(m1), and wet(m1)), the logical rules of inference (including a forward chain operation), and a subset of the defeasible rules of inference (i.e. the listener assumes that Rule A features in every candidate argument system considered by the speaker). However, there are two other inferential rules -Rules B, and C from above -the status of which the speaker is uncertain: elements of Z may individually feature one, both, or neither of these rules.", |
| "cite_spans": [ |
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| "start": 248, |
| "end": 249, |
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| "section": "Illustration", |
| "sec_num": "3.1" |
| }, |
| { |
| "text": "For this illustration, assume that the listener has observed the speaker utter (5). Intuitively, this utterance conveys a high degree of speaker commitment to the prejacent (lit(m1)), but it should also convey something to the listener about the speaker's argument system uncertainty: since it is established that the speaker recognizes that wet(m1), in uttering (5) the speaker has signalled that she finds it unlikely that Rule B is a relevant premise in this context.", |
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| "sec_num": "3.1" |
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| { |
| "text": "The pragmatic listener must infer the value of Z under uncertainty; that is, she will not know the precise proportion of elements of Z that contain inferential Rules B and/or C (or neither). In other words, let \u03b2 be the speaker's degree of belief that Rule B is in the contextually-relevant argument system; and let \u03b3 stand in for speaker beliefs about Rule C. The pragmatic listener updates her beliefs about the values of \u03b2 and \u03b3 by observing the speaker's utterance production choices in context, in addition to inferring the value of the threshold \u03b8. For this illustration, I assume uniform prior beliefs over values for \u03b2, \u03b3, and \u03b8 and make the simplyfing assumption that C(must) is equal to 1 while the null message has zero cost. 9 I arbitrarily set the optimality parameter \u03b1 to 4.", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "Illustration", |
| "sec_num": "3.1" |
| }, |
| { |
| "text": "In the computational implementation of this example, 10,000 samples are drawn from P L 1 (\u03b2, \u03b3, \u03b8|must( lit(m1))) using Markov Chain Monte Carlo sampling, with the assumption that the contextually-salient argument A is A 1 . 10 Marginal posterior distributions over values for the inferred parameters are presented in 1. As a sanity check, we see that the posterior over values of \u03b3 is effectively uniform. This is exactly what is to be expected, as the inclusion of Rule C in the argument system has no bearing on the justifiability of concluding lit(m1); thus, the speaker's production of (5) is not informative for the listener regarding the status of Rule C. However, the posterior over values of \u03b2 suggests that the listener has learned something regarding the speaker's beliefs about Rule B.", |
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| "ref_spans": [], |
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| "section": "Illustration", |
| "sec_num": "3.1" |
| }, |
| { |
| "text": "Recall that the presence of this inferential rule in the argument system has the consequence that match(x) \u2227 strike(x) > lit(x) , lit(m1) is not justified (given our assumptions about the ground formulae and possible rules of inference from above). But must-lit(m1) was asserted on the basis of argument match(x) \u2227 strike(x) > lit(x); thus, after observing the speaker produce (5), the listener considers it relatively unlikely that the speaker expects Rule Bmatch(x) \u2227 strike(x) \u2227 wet(x) > \u00aclit(x) -to be a relevant inferential rule.", |
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| "ref_spans": [], |
| "eq_spans": [], |
| "section": "Illustration", |
| "sec_num": "3.1" |
| }, |
| { |
| "text": "On this picture, disagreement functions differently than on analyses characterized by the credence assumption. On that assumption, we could understand disagreements over must \u03c6 as stemming from interlocutors' differences regarding their (deterministic) beliefs about the status of the premises or regarding the relationship of the premises to \u03c6. The probabilistic enrichment explored here makes the story slightly more complicated. Consider the illustration above: a listener who hears a speaker utter (5) in this context is likely to disagree with that speaker, if the listener's own uncertainty in-volves high expectation that Rule B is relevant for the purposes of inference (and hence the listener has relatively low commitment to the prejacent, the match is lit). But what is the source of the disagreement? It cannot be that the listener knows definitively that she and the speaker have drastically different expectations regarding what inferential premises can be relied on in this context. However, the speaker's production of (5) is highly suggestive of such a difference: it is quite likely that the speaker puts relatively little weight in the chance that wet matches will light, even when struck. As a consequence, it is quite likely that the speaker has a high degree of belief that the match is lit. Disagreement, then, is triggered by the listener being fairly certain that her argument system uncertainty -her internal Z distribution -is substantially different from her interlocutor's. 11 This suggests a way of understanding context and communicative exchange that complements the conventional \"common ground\" approach of Stalnaker (2002) , whereby context records the propositions that interlocutors accept ('treat as true'), and communicative exchange involves proposals to update this common ground via addition of new propositions. In particular, my analysis suggests a means of formally modeling another layer of the context concerned with the uncertainty that interlocutors bring to bear on propositions not necessarily treated as categorically true. Epistemic linguistic constructions (e.g. must) facilitate coordination of this uncertainty between interlocutors, by communicating properties of this uncertainty from a particular epistemic vantage point.", |
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| "end": 1656, |
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| "section": "Discussion and conclusion", |
| "sec_num": "4" |
| }, |
| { |
| "text": "vonFintel and Gillies (2010), for example, contend that must \u03c6 presupposes that \u03c6 has not yet been settled in context.3 Or perhaps Mary agrees with Ann on the premises but disagrees regarding their relationship to the conclusion.", |
| "cite_spans": [], |
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| { |
| "text": "I focus on Stone's argument system semantics because his formalism provides a way of verifying the relationship between a conclusion and the premises that condition it. This is crucial for my analysis, which captures how listeners infer speaker beliefs about premises having only observed conclusions asserted by the speaker. But similar results could be achievable with other semantic 'backends'.", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "", |
| "sec_num": null |
| }, |
| { |
| "text": "This example is based largely on one fromStone (1994).", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "", |
| "sec_num": null |
| }, |
| { |
| "text": "That is, on this analysis, every individual argument system is assumed to have uniform probability. Alternatively, as a reviewer suggests, one could suppose that some elements of Z are more likely than others a priori (and that the truth conditions of must \u03c6 are sensitive to this non-uniform prior).", |
| "cite_spans": [], |
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| { |
| "text": "I followLassiter and Goodman (2013) in introducing this null utterance choice, which is an implementational necessity in the absence of utterance alternatives. Adding plausible linguistic alternatives to the model -including might \u03c6 and bare \u03c6 -does not drastically alter the patterns presented here.", |
| "cite_spans": [], |
| "ref_spans": [], |
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| "sec_num": null |
| }, |
| { |
| "text": "The prior distributions over values for \u03b2, \u03b3, and \u03b8 are discrete distributions with uniform probability mass on 11 evenly-spaced values on the interval [0, 1].10 The implementation was programmed using WebPPL (Goodman and Stuhlm\u00fcller, 2014). Code is available at https://github.com/bwaldon/probmust.", |
| "cite_spans": [], |
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| "sec_num": null |
| }, |
| { |
| "text": "A more precise understanding of modal disagreement in this framework -for example, how do we quantify the conditions giving rise to disagreement? -is left to future work.", |
| "cite_spans": [], |
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| "text": "Marginal posterior distributions over values of \u03b2, listener beliefs about the speaker's expectation that Rule B is in the contextually-relevant argument system; \u03b3, listener beliefs about the speaker's expectation that Rule C is in this state; \u03b8, the threshold for must, and speaker commitment to lit(m1) on the basis of inferential rule A, calculated by approximating a posterior distribution over values of Z from posterior values of \u03b2 and \u03b3. Degree of speaker commitment is anti-correlated with \u03b2 and not correlated with \u03b3.", |
| "type_str": "figure" |
| } |
| } |
| } |
| } |
