Linguistic interpretation as inference under argument system uncertainty: the case of epistemic must (2020)

Abstract: Modern semantic analyses of epistemic language (incl. the modals must and might) can be characterized by the following ‘credence assumption’: speakers have full certainty regarding the propositions that structure their epistemic state. Intuitively, however: a) speakers have graded, rather than categorical, commitment to these propositions, which are often never fully and explicitly articulated; b) listeners have higher-order uncertainty about this speaker uncertainty; c) must p is used to communicate speaker commitment to some conclusion p 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). The analysis makes desirable predictions regarding the behavior and interpretation of must, and it suggests a new way of considering the nature of context and communicative exchange.

## introduction 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: 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. 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 φ appear to mark weak speaker commitment to the prejacent compared to the unmodalized counterpart, 'bare' φ. the observation stems from consideration of contexts such as (2): 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 φ 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 φ -unlike bare φ -allows for the possibility that ¬φ 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 φ is incompatible with ¬φ, and must's infelicity in (2) is a consequence of a violation of independently-stipulated felicity conditions. @xcite 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. 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): 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. ## probabilistic argument system semantics 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. @xcite we can then define speaker commitment to a proposition φ on the basis of some argument a as the likelihood that a, φ justifies φ given possible argument systems in z. must φ, then, is a comment on this likelihood value: if the likelihood exceeds a certain contextually-specified threshold, then the statement is true: speakers produce must φ to convey their degree of belief that φ 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 φ, then, allows the listener to update her uncertainty about the speaker's z distribution. the speaker's production of must φ 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 φ can be computed). 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 θ. following lassiter and goodman (2013), who model interpretation of gradable adjectives using a threshold-based semantics, i assume that this θ variable is passed from l 0 and eventually estimated by the pragmatic l 1 listener (defined below) from a prior distribution over values of θ. 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, α 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. 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 θ: thus, interpretation of must is a joint inference about the state of the world (speaker beliefs regarding the justifiability of concluding φ) and the value of a semantic threshold variable θ. these speaker beliefs -p a, φ 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. ## discussion and conclusion on this picture, disagreement functions differently than on analyses characterized by the credence assumption. on that assumption, we could understand disagreements over must φ as stemming from interlocutors' differences regarding their (deterministic) beliefs about the status of the premises or regarding the relationship of the premises to φ. 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. @xcite 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.