Base_JSON/prefixS/json/scil/2020.scil-1.29.json

{
    "paper_id": "2020",
    "header": {
        "generated_with": "S2ORC 1.0.0",
        "date_generated": "2023-01-19T15:38:43.963262Z"
    },
    "title": "Modeling Behavior in Truth Value Judgment Task Experiments",
    "authors": [
        {
            "first": "Brandon",
            "middle": [],
            "last": "Waldon",
            "suffix": "",
            "affiliation": {
                "laboratory": "",
                "institution": "Stanford University",
                "location": {}
            },
            "email": "[email protected]"
        },
        {
            "first": "Judith",
            "middle": [],
            "last": "Degen",
            "suffix": "",
            "affiliation": {
                "laboratory": "",
                "institution": "Stanford University",
                "location": {}
            },
            "email": "[email protected]"
        }
    ],
    "year": "",
    "venue": null,
    "identifiers": {},
    "abstract": "Truth Value Judgment Task experiments (TVJTs) are a common means of investigating pragmatic competence, particularly with regards to scalar inference. We present a novel quantitative linking function from pragmatic competence to participant behavior on TVJTs, based upon a Bayesian probabilistic model of linguistic production. Our model captures a range of observed phenomena on TVJTs, including intermediate responses on a nonbinary scale, population and individual-level variation, participant endorsement of false utterances, and variation in response due to socalled scalar diversity.",
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        "paper_id": "2020",
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        "abstract": [
            {
                "text": "Truth Value Judgment Task experiments (TVJTs) are a common means of investigating pragmatic competence, particularly with regards to scalar inference. We present a novel quantitative linking function from pragmatic competence to participant behavior on TVJTs, based upon a Bayesian probabilistic model of linguistic production. Our model captures a range of observed phenomena on TVJTs, including intermediate responses on a nonbinary scale, population and individual-level variation, participant endorsement of false utterances, and variation in response due to socalled scalar diversity.",
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                "section": "Abstract",
                "sec_num": null
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                "text": "In Truth Value Judgment Task experiments (TJVTs), participants are asked whether a given sentence is, e.g., 'right' or 'wrong' (or 'true' or 'false', etc.) , often in a context of evaluation. In the field of experimental pragmatics, participant judgments in TVJT paradigms have been particularly important for investigating pragmatic competence, especially as it relates to scalar implicature (Noveck, 2001; Noveck and Posada, 2003; Bott and Noveck, 2004; De Neys and Schaeken, 2007; Geurts and Pouscoulous, 2009; Chemla and Spector, 2011; Degen and Goodman, 2014; Degen and Tanenhaus, 2015) . On the traditional view of pragmatic competence and its link to TVJT responses, scalar implicature is assumed -following Grice (1975) -to be a binary and categorical phenomenon, in the sense that a given utterance is assumed to categorically either give rise to an implicature or not, depending on contextual, cognitive, and linguistic factors. To experimentalists operating on this assumption, a participant's judgment on a particular trial in a TVJT reflects whether or not a scalar implicature was computed in context. For example, a 'wrong' judgment of the sentence John ate pizza or a sandwich, in a context in which the stronger utterance alternative John ate pizza and a sandwich is true and equally relevant, is typically interpreted as a \"pragmatic\" judgment: participants must have recognized that in such a context, the or-sentence is true yet underinformative. Pragmatically enriching it to John didn't eat both pizza and a sandwich via scalar inference makes it contextually false. Conversely, an answer of 'right' on this view reflects a \"literal\" semantic interpretation whereby the implicature is not computed (i.e. John ate pizza or a sandwich -and possibly both).",
                "cite_spans": [
                    {
                        "start": 108,
                        "end": 155,
                        "text": "'right' or 'wrong' (or 'true' or 'false', etc.)",
                        "ref_id": null
                    },
                    {
                        "start": 393,
                        "end": 407,
                        "text": "(Noveck, 2001;",
                        "ref_id": "BIBREF18"
                    },
                    {
                        "start": 408,
                        "end": 432,
                        "text": "Noveck and Posada, 2003;",
                        "ref_id": "BIBREF19"
                    },
                    {
                        "start": 433,
                        "end": 455,
                        "text": "Bott and Noveck, 2004;",
                        "ref_id": "BIBREF0"
                    },
                    {
                        "start": 456,
                        "end": 483,
                        "text": "De Neys and Schaeken, 2007;",
                        "ref_id": "BIBREF2"
                    },
                    {
                        "start": 484,
                        "end": 513,
                        "text": "Geurts and Pouscoulous, 2009;",
                        "ref_id": "BIBREF9"
                    },
                    {
                        "start": 514,
                        "end": 539,
                        "text": "Chemla and Spector, 2011;",
                        "ref_id": "BIBREF1"
                    },
                    {
                        "start": 540,
                        "end": 564,
                        "text": "Degen and Goodman, 2014;",
                        "ref_id": "BIBREF3"
                    },
                    {
                        "start": 565,
                        "end": 591,
                        "text": "Degen and Tanenhaus, 2015)",
                        "ref_id": "BIBREF5"
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                ],
                "ref_spans": [],
                "eq_spans": [],
                "section": "Introduction",
                "sec_num": "1"
            },
            {
                "text": "This linking assumption underpins the vast majority of TVJT literature relating to scalar inference (Noveck, 2001; Papafragou and Musolino, 2003; Geurts and Pouscoulous, 2009; Doran et al., 2012; Potts et al., 2015) . In an early example, Papafragou and Musolino (2003) observe that children accept true but underinformative sentences in a TVJT at a relatively high rate relative to adults, and that this rate is modulated by the particular linguistic scale invoked on a given trial of the experiment (i.e. some/all vs. finish/start vs. cardinal numbers). The authors argue from this result that scalar implicature computation is dependent upon linguistic scale as well as on a child's recognition of the communicative goals of her interlocutor.",
                "cite_spans": [
                    {
                        "start": 100,
                        "end": 114,
                        "text": "(Noveck, 2001;",
                        "ref_id": "BIBREF18"
                    },
                    {
                        "start": 115,
                        "end": 145,
                        "text": "Papafragou and Musolino, 2003;",
                        "ref_id": "BIBREF20"
                    },
                    {
                        "start": 146,
                        "end": 175,
                        "text": "Geurts and Pouscoulous, 2009;",
                        "ref_id": "BIBREF9"
                    },
                    {
                        "start": 176,
                        "end": 195,
                        "text": "Doran et al., 2012;",
                        "ref_id": "BIBREF6"
                    },
                    {
                        "start": 196,
                        "end": 215,
                        "text": "Potts et al., 2015)",
                        "ref_id": "BIBREF21"
                    },
                    {
                        "start": 239,
                        "end": 269,
                        "text": "Papafragou and Musolino (2003)",
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                ],
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                "section": "Introduction",
                "sec_num": "1"
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            {
                "text": "Though widely employed, this linking assumption for TVJTs is associated with a host of problems discussed by Jasbi et al. (2019) . Following those authors as well as Tanenhaus (2004), we take these open problems to be indicative of a larger issue in linguistics, namely that the linking hypotheses which bridge linguistic theory and experimentally-elicited behavior are often underdeveloped, underspecified, or (in some cases) absent in experimental studies. In the service of providing a proof of concept for how this is-sue may be addressed by future researchers, we propose and evaluate a novel account of participant response in TVJT paradigms based on an explicit and quantitatively specified linking function rooted in a probabilistic theory of pragmatic competence. The general idea is that participants' responses in TVJT experiments are related to the probability with which a cooperative pragmatic speaker would have produced the observed utterance (e.g., John ate pizza or a sandwich) in order to communicate the meaning presented to participants as fact (e.g., that John ate both pizza and a sandwich). This probabilistic production based view departs substantially from the previous widespread assumption that truth-value judgments are a measure of interpretation.",
                "cite_spans": [
                    {
                        "start": 109,
                        "end": 128,
                        "text": "Jasbi et al. (2019)",
                        "ref_id": "BIBREF14"
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                ],
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                "eq_spans": [],
                "section": "Introduction",
                "sec_num": "1"
            },
            {
                "text": "Before turning to the specifics of the account, we briefly review some of the open problems in the TVJT literature that motivate the re-thinking of linking functions in TVJT paradigms:",
                "cite_spans": [],
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                "section": "Introduction",
                "sec_num": "1"
            },
            {
                "text": "Intermediate judgments: When provided more than two response options in a TVJT, a sizable proportion of participants rates underinformative sentences using the intermediate response options -for example, as only 'kind of [right / wrong]', or 'neither [right nor wrong]'. Katsos and Bishop (2011), for example, provided participants with three response options and observed substantial selection of the intermediate option. They interpreted the choice of this intermediate option as being the result of the computation of an implicature, but a priori, there is no reason to favor this linking assumption over one whereby the intermediate response is associated with a literal semantic interpretation. More generally, it is not clear how the outputs of a binary model of scalar implicature (i.e. implicature or \u00acimplicature) should relate to non-binary responses on TVJTs.",
                "cite_spans": [],
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                "eq_spans": [],
                "section": "Introduction",
                "sec_num": "1"
            },
            {
                "text": "Population-level variation: In order to explain behavioral variation in contexts where one expects a scalar inference, an adherent to the categorical view of scalar implicature must stipulate that a) not all participants calculated the implicature; or b) some participants who calculated the implicature showed divergent behavior due to some independent mechanism which masked the 'correct' implicature behavior; or some combination of (a) and (b). However, and despite the prevalence of variation at the population level in reported TVJT experiments, even a qualitative analysis of this kind of variation is largely absent from the experimental scalar implicature literature. Scalar diversity: Doran et al. (2012) , following Papafragou and Musolino (2003) inter alia, report that judgments of true but underinformative sentences vary according to the particular linguistic material contained within the sentence, in particular the relevant linguistic scale. They conclude that variation among scalar implicatures is a function of the scale itself (see also van Tiel et al. 2014 for further support for scale-based scalar diversity in a non-TVJT paradigm).",
                "cite_spans": [
                    {
                        "start": 695,
                        "end": 714,
                        "text": "Doran et al. (2012)",
                        "ref_id": "BIBREF6"
                    },
                    {
                        "start": 727,
                        "end": 757,
                        "text": "Papafragou and Musolino (2003)",
                        "ref_id": "BIBREF20"
                    }
                ],
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                "section": "Introduction",
                "sec_num": "1"
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                "text": "Whether this variation is truly due to inherent features of the linguistic scale (or, e.g., prior world knowledge, or other linguistic material, or other confounding features of the experimental context) is an open question which warrants investigation beyond the scope of this paper. Below, we analyze data from a TVJT where different rates of exhaustive interpretation were observed between a putative lexical scale (<and, or>) and a putative ad-hoc, context-dependent pragmatic scale. Our analysis of the data suggests that in this instance, (at least some) variation at the level of linguistic scale may be reduced to more general aspects of pragmatic competence.",
                "cite_spans": [],
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                "section": "Introduction",
                "sec_num": "1"
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            {
                "text": "Endorsement of false utterances: Invariably, a proportion of participants in TVJTs accepts strictly false sentences. For example, in the study we analyze below, a substantial number of participants rated conjunctions A^B as partially correct in contexts where only A was true. The most common approaches to this type of data are either to use it as the basis of an exclusion criterion or to simply consider it meaningless noise. Doran et al. (2012) , for example, exclude participants whose performance deviates by more than two standard deviations from the mean response on 'control' sentences whose semantic contents are consistent with the context of evaluation (and which do not admit of potentially contradictory pragmatic enrichments) or whose semantic contents contradict the context. Katsos and Bishop (2011) report that 2.5% of false sentences in their experiment were endorsed by child participants. On the standard linking assumption, these data are difficult to make sense of, but we will show that they are within the scope of a satisfactory analysis of TVJT behavior.",
                "cite_spans": [
                    {
                        "start": 429,
                        "end": 448,
                        "text": "Doran et al. (2012)",
                        "ref_id": "BIBREF6"
                    },
                    {
                        "start": 792,
                        "end": 816,
                        "text": "Katsos and Bishop (2011)",
                        "ref_id": "BIBREF16"
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                ],
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                "section": "Introduction",
                "sec_num": "1"
            },
            {
                "text": "The remainder of the paper is structured as follows: in Section 2, we summarize the results of a recently reported TVJT study that exemplifies the features discussed above: intermediate judgments, population-level variation, scalar diversity, and participant endorsement of false utterances. Section 3 presents our novel quantitative model of the data from that study. Building on insights from the Bayesian probabilistic literature on pragmatic competence (Frank and Goodman, 2012; Goodman and Stuhlm\u00fcller, 2013), we model participants as making judgments about a soft-optimal pragmatic speaker whose production choices are a function of utterances' contextual informativeness. On our analysis, participants furthermore expect that the speaker sometimes produce strictly false utterances that are nonetheless somewhat contextually useful. We show that this analysis provides broader empirical coverage over the traditional assumptions discussed above. 1 2 TVJT Data 2.1 Experiment Materials, Design and Procedure Jasbi et al. (2019) report the results of a TVJT designed to test whether linking hypothesis and number of response options modulate the researcher's inferences about scalar implicature rates. In their study, number of response options varied between two and five as a between-subjects manipulation. Conditions are summarized in Figure 1 . Participants (n = 200) were first shown six cards (Table  2) featuring one or two of the following animals: a cat, a dog, and an elephant. On every trial, participants saw one of the six cards, and a blindfolded cartoon character Bob made guesses as to what animals were on the card. Participants were asked to rate Bob's guesses using the response options available in their particular condition.",
                "cite_spans": [],
                "ref_spans": [
                    {
                        "start": 1343,
                        "end": 1351,
                        "text": "Figure 1",
                        "ref_id": "FIGREF0"
                    },
                    {
                        "start": 1404,
                        "end": 1414,
                        "text": "(Table  2)",
                        "ref_id": "TABREF1"
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                ],
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                "section": "Introduction",
                "sec_num": "1"
            },
            {
                "text": "Bob made the following guess types: simple declaratives (e.g., There is a cat), conjunctions (e.g., There is a cat and a dog), and disjunctions (e.g., There is a cat or a dog). Card types were crossed with guess types in this study such that a card containing an animal X could be presented with a guess of There is an X, There is an X or a Y (where Y is some animal distinct from X), There is an X and a Y, or There is a Y; cards containing two animals X and Y could be presented with a guess of There is an X, There is an X or a Y, There is an X and a Y, or There is a Z (where Z is some animal distinct from X and Y).",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "Introduction",
                "sec_num": "1"
            },
            {
                "text": "The researchers elicited 3 judgments per participant for each combination of card and guess type.",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "Introduction",
                "sec_num": "1"
            },
            {
                "text": "Proportions of responses for each card-guess type in each response-option condition are shown in Figure 1 , with rows presenting behavior aggregated across one and two-card conditions.",
                "cite_spans": [],
                "ref_spans": [
                    {
                        "start": 97,
                        "end": 105,
                        "text": "Figure 1",
                        "ref_id": "FIGREF0"
                    }
                ],
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                "section": "Results and Discussion",
                "sec_num": "2.2"
            },
            {
                "text": "The results of the study illustrate the several open empirical issues associated with TVJTs more generally. First, participants routinely reported intermediate judgments between 'Right' and 'Wrong' in those conditions where intermediate response options were available. In the Quaternary and Quinary response-option conditions, for example, the intermediate judgment of 'Kinda Right' was the single most-selected response option in two-animal card conditions where Bob's guess was true but underinformative (i.e. either a simple delcarative or a disjunction).",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "Results and Discussion",
                "sec_num": "2.2"
            },
            {
                "text": "The results also exemplify the issue of population-level variation: for example, although behavioral patterns are otherwise fairly categorical in the Binary condition, participant judgments were roughly split between 'Right' and 'Wrong' for underinformative uses of disjunction on two-animal card conditions. A visual inspection of the results suggests even more variation in the population as number of response options increase. The authors furthermore reported individual-level variation: qualitatively similar trials (e.g. two trials involving underinformative disjunction) sometimes received different re- sponses from the same participant.",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "Results and Discussion",
                "sec_num": "2.2"
            },
            {
                "text": "Comparison of judgments of true but underinformative simple declaratives (i.e. There is an X) to judgments of true but underinformative disjunctions (i.e. There is an X or a Y) on two-animal card conditions revealed some amount of scalar diversity. Following Horn (1972) , exposure to the disjunctive connective or canonically activates an informationally-stronger scalemate and as a pragmatic alternative to give rise to an exclusive interpretation. In contrast, the pragmatic scale in the case of the simple declarative is constructed in a more context-dependent manner. To illustrate, in a two-animal card context where the card features both a cat and a dog, the listener considers a partially-ordered pragmatic scale of cat and dog, cat, and dog, where the conjunction outranks its scalemates in terms of informational strength. Thus, an utterance of cat activates cat and dog as an alternative to give rise to an the exhaustive interpretation (There is only a cat on the card).",
                "cite_spans": [
                    {
                        "start": 259,
                        "end": 270,
                        "text": "Horn (1972)",
                        "ref_id": "BIBREF13"
                    }
                ],
                "ref_spans": [],
                "eq_spans": [],
                "section": "Results and Discussion",
                "sec_num": "2.2"
            },
            {
                "text": "In the Binary and Ternary conditions, under-informative uses of or resulted in substantially higher rates of 'Wrong' responses than did underinformative simple declaratives, suggesting that at the population level, or was interpreted more exhaustively than the simple declarative. However, this pattern was reversed in the Quaternary and Quinary conditions, in which underinformative simple declaratives were more likely to be considered only 'Kinda Right' and less likely to be considered simply 'Right' compared to underinformative disjunctions. This pattern suggests that in the Quaternary and Quinary conditions, simple declaratives were interpreted more exhaustively than disjunctions. Finally, the data in the Quaternary and Quinary conditions also reveal substantial participant endorsement of false utterances. Note specifically that in one-animal card trials, the conjunctive guess (e.g. cat and dog) is strictly false; thus, we might na\u00efvely expect a priori that participants categorically judge these utterances to be 'Wrong' in all conditions. Yet when given the option to rate this sentence 'Kinda Right' or 'Kinda Wrong', participants often did so. In all other conditions where the utterance was strictly false (e.g. a guess of elephant for a card containing a cat or a cat and dog), behavior was effectively categorical. That is, rates of endorsement of false utterances varied according to the particular way in which the sentence was false in context.",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "Results and Discussion",
                "sec_num": "2.2"
            },
            {
                "text": "In sum, the data collected by Jasbi et al. (2019) reflect a range of behavioral patterns unaccounted for by the traditional categorical view of scalar inference and corresponding standard linking assumptions. Below, we report an analysis of their data that aims to predict these phenomena.",
                "cite_spans": [],
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                "section": "Results and Discussion",
                "sec_num": "2.2"
            },
            {
                "text": "3.1 Cognitive model Our analysis implements a proposal outlined by Jasbi et al. (2019) , couched in the Rational Speech Act (RSA) framework (Frank and Goodman, 2012; Goodman and Stuhlm\u00fcller, 2013). RSA provides a Bayesian, probabilistic account of pragmatic competence. In RSA, the pragmatic inferences drawn by listeners are represented as probability distributions over meanings which the speaker plausibly intended to convey with a given observed utterance. The probability of this listener (L 1 ) attributing an intended meaning m to a speaker who produces an utterance u is calculated from a prior probability distribution over potential world states P w as well as from L 1 's expectations about the linguistic behavior of the speaker S 1 .",
                "cite_spans": [
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                        "start": 67,
                        "end": 86,
                        "text": "Jasbi et al. (2019)",
                        "ref_id": "BIBREF14"
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                ],
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                "section": "Analysis",
                "sec_num": "3"
            },
            {
                "text": "P L 1 (m|u) / P S 1 (u|m) \u2022 P w (m)",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "Analysis",
                "sec_num": "3"
            },
            {
                "text": "P S 1 is modeled as a probability distribution over possible utterances given the speaker's communicative intentions m. This speaker produces utterances that soft-maximize utility, where utility is defined via a tradeoff between an utterance's cost C and its contextual informativeness, calculated from the representation of a literal listener L 0 whose interpretation of an utterance u is in turn a function of the truth conditional meaning [[u] ](m) and of her prior expectations P w (m) regarding the likelihood of possible world states. The extent to which the speaker maximizes utility is modulated by a parameter \u21b5 -the greater \u21b5, the more the speaker produces utterances that maximize utility.",
                "cite_spans": [
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                        "text": "[[u]",
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                "section": "Analysis",
                "sec_num": "3"
            },
            {
                "text": "P S 1 (u|m) / e \u21b5(ln L 0 (m|u) C(u)) P L 0 (m|u) / [[u]](m) \u2022 P w (m)",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "Analysis",
                "sec_num": "3"
            },
            {
                "text": "In RSA (and contra the traditional view), prag-matic inferences are not categorical computations of enriched meanings over the semantic denotations of utterances. For example, exclusive interpretations of or are represented in RSA as a positive shift in the posterior probability of an exclusive meaning, relative to its prior probability.",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "Analysis",
                "sec_num": "3"
            },
            {
                "text": "In other words, 'implicature' is not a theoretical construct in the RSA framework, absent additional stipulations regarding how to go from probability distributions to binary, categorical inferences. This is an advantage: providing a probabilistic representation of both the speaker's utterance choices and the listener's resulting posterior beliefs after observing an utterance puts us one step closer to accounting for the quantitative behavioral patterns observed in tasks such as TVJTs.",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "Analysis",
                "sec_num": "3"
            },
            {
                "text": "Jasbi et al. 2019proposed but did not systematically test a simple linking hypothesis: rather than providing one response if an implicature is computed and another if it isn't, a participant in a TVJT experiment provides a particular response to an utterance u if the probability of u given a meaning represented by m lies within a particular probability interval on the distribution P S 1 (u|m). 2 The participant is modeled as a responder R, who in a binary forced-choice task between 'Right' and 'Wrong' responds 'Right' to an utterance u in world m just in case P S 1 (u|m) meets or exceeds some probability threshold \u2713:",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "Behavioral model",
                "sec_num": "3.2"
            },
            {
                "text": "R(u, m, \u2713) = ( 'Right' iff P S 1 (u|m) \u2713 'Wrong' otherwise",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "Behavioral model",
                "sec_num": "3.2"
            },
            {
                "text": "The model is extended straightforwardly to an experiment in which participants have a third response option (e.g. 'Neither'), as in the Ternary condition. In this case, the model specifies two probability thresholds: \u2713 1 , the minimum standard for an utterance in a given world state to count as 'Right', and \u2713 2 , the minimum standard for 'Neither'. Thus, in the Ternary condition:",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "Behavioral model",
                "sec_num": "3.2"
            },
            {
                "text": "R(u, m, \u2713) = 8 > < > : 'Right'",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "Behavioral model",
                "sec_num": "3.2"
            },
            {
                "text": "iff P S 1 (u|m) \u2713 1 'Neither' iff \u2713 1 > P S 1 (u|m) \u2713 2 'Wrong' otherwise Applying a similar logic allows for the specification of linking hypotheses for TVJTs with an arbitrary number of response options.",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "Behavioral model",
                "sec_num": "3.2"
            },
            {
                "text": "The intuition behind the threshold model is as follows: participants should disprefer utterances that are relatively unexpected. Thus, high S 1 production probability for a given utterance in context makes it more likely that the utterance receives a positive evaluation in the TVJT -expressed by ordered response options above 'Wrong'. Conversely, the more unexpected an utterance is, the more likely it is to be judged as 'Wrong'. Underinformative utterances of the sort that have traditionally been used to assess 'implicature rates' are precisely the kinds of utterances that are unexpected from informative speakers and are therefore likely to be rated as 'Wrong'.",
                "cite_spans": [],
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                "eq_spans": [],
                "section": "Behavioral model",
                "sec_num": "3.2"
            },
            {
                "text": "Here, we assess the quality of this linking hypothesis on the dataset from Jasbi et al. (2019) . To that end, we first specify the space of possible meanings and utterances that inform a participant's pragmatic competence in this task. We assume that participants have uniform prior expectations of seeing any of the six possible cards in the experiment. We further assume that participants have uniform prior expectations of a speaker producing any of the four utterance types with which a card may have been crossed. For example, if the card featured either just a cat or both a cat and a dog, we represent the participant as having uniform prior expectations of a speaker producing the guesses elephant, cat, dog, cat and dog, or cat or dog (that is, we do not posit a cost asymmetry between possible utterances). 3 For illustrative purposes, the 'Simple Bayesian' bars in Figure 2 display marginal distributions over possible utterances produced by S 1 given these assumptions for the utterance and meanings priors, as well as an arbitary value of 1 for the optimality parameter \u21b5, and given that the speaker intends either to communicate the meaning that (just) a cat is on the card or that both a cat and a dog are. The speaker distributions reveal two conceptual issues for the threshold response model proposed by Jasbi et al (2019) .",
                "cite_spans": [
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                        "text": "Jasbi et al. (2019)",
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                        "text": "3",
                        "ref_id": null
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                ],
                "ref_spans": [
                    {
                        "start": 876,
                        "end": 884,
                        "text": "Figure 2",
                        "ref_id": "FIGREF1"
                    }
                ],
                "eq_spans": [],
                "section": "Behavioral model",
                "sec_num": "3.2"
            },
            {
                "text": "First, the probability of S 1 producing the strictly false guess of cat and dog should be zero if the card contains just a cat. This is because the literal listener probability P L 0 of inferring the 'only cat' meaning given cat and dog is zero by virtue of the fact that the utterance is strictly false in this world state. Thus, any model of response that is a function of P S 1 as specified predicts that participants categorically rate the cat and dog guess as 'Wrong' in this context, contrary to what is observed in the Quaternary and Quinary conditions.",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "Behavioral model",
                "sec_num": "3.2"
            },
            {
                "text": "Second, the probability of producing disjunctions is lower than the probability of producing simple declarative guesses in two-animal card contexts. This asymmetry is advantageous in the case of the Binary and Ternary response data: assuming a threshold for 'Right' positioned between P S 1 (cat or dog|cat and dog) and P S 1 (cat|cat and dog), we predict correctly that underinformative simple declaratives should be judged 'Right' more often than underinformative disjunctions. But the asymmetry in S 1 probabilities therefore predicts the wrong pattern of responses on corresponding trials in the Quaternary and Quinary conditions.",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "Behavioral model",
                "sec_num": "3.2"
            },
            {
                "text": "We argue that these two seemingly disparate issues can be mediated by a common solution.",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "Behavioral model",
                "sec_num": "3.2"
            },
            {
                "text": "In particular, we propose a revision to the simple Bayesian inference story above, whereby pragmatically-competent listeners either expect speaker productions as directly sampled from the P S 1 distribution, or that those utterance production probabilities inform a second conditional probability distribution of utterances given utterances, the 'Partial Truth' utterance distribution P S P T :",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "Behavioral model",
                "sec_num": "3.2"
            },
            {
                "text": "P S P T (u 0 |u) / P m2JuK P S 1 (u 0 |m) 4",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "Behavioral model",
                "sec_num": "3.2"
            },
            {
                "text": "The 'Partial Truth' distribution is a generalized way of modeling a speaker who makes assertions that are sometimes strictly false in light of her intended meaning. Recall that the semantic content of any possible utterance choice made by S 1 is a set of possible worlds and is therefore consistent with meanings unintended by the speaker. S P T models the speaker's soft-optimal production probabilities given these unintended meanings, renormalizing the pragmatic speaker's production probabilities over all possible worlds consistent with utterance choices sampled from P S 1 . To illustrate: suppose a speaker intends to communicate that many (but not all) of the X are Y, and has quantifier choices many and all. The only possible utterance choice for the simple Bayesian S 1 speaker is many, which is semantically consistent with the intended meaning. But the lowerbounded quantifier many is also semantically consistent with an 'all of the X are Y' meaning, which in turn is consistent with the utterance choice all. By S P T , we have some nonzero expectation that the speaker will use all to communicate the 'many (but not all) of the X are Y' meaning. 5 Thus, a pragmatic listener who hears all from the 'Partial Truth' speaker will have a nonzero expectation that all should receive an imprecise, non-maximal interpretation. In other words, S P T provides a generalized way of formalizing 'loose-talk' production behavior (Lasersohn, 1999) . 6 The 'Partial Truth' bars in Figure 2 visualize marginal distributions over utterances given an arbitrary 0.6 probability that the speaker samples from the P S P T distribution after sampling from P S 1 . The 'Partial Truth' speaker assigns nonzero probability to a guess of cat and dog even when the speaker's intended meaning is the single-animal cat card, largely due to the fact that the optimal guess in this context (cat) is truthconditionally consistent with a two-animal card that makes cat and dog both true and pragmatically optimal. 7 Moreover, this speaker assigns 5 The effect of this is similar to the use of QUD projection functions for hyperbolic interpretations (Kao et al., 2014) .",
                "cite_spans": [
                    {
                        "start": 1433,
                        "end": 1450,
                        "text": "(Lasersohn, 1999)",
                        "ref_id": "BIBREF17"
                    },
                    {
                        "start": 1453,
                        "end": 1454,
                        "text": "6",
                        "ref_id": null
                    },
                    {
                        "start": 2133,
                        "end": 2151,
                        "text": "(Kao et al., 2014)",
                        "ref_id": "BIBREF15"
                    }
                ],
                "ref_spans": [
                    {
                        "start": 1483,
                        "end": 1491,
                        "text": "Figure 2",
                        "ref_id": "FIGREF1"
                    }
                ],
                "eq_spans": [],
                "section": "Behavioral model",
                "sec_num": "3.2"
            },
            {
                "text": "6 Formalizing this production behavior is different from analyzing why imprecision exists (indeed, is pervasive) in linguistic communication. For the time being, we present this 'loose-talk' speaker model without a thorough assessment of its explanatory power.",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "Behavioral model",
                "sec_num": "3.2"
            },
            {
                "text": "7 Because cat or dog is a possible S1 production, and this choice lies in an entailment relation with the simple declar-greater probability to a guess of cat or dog in twoanimal contexts and down-weights the probability of producing simply cat: the optimal utterance in this context (cat and dog) is consistent with several world states in which the disjunction cat or dog is assertable and with relativley fewer worlds in which cat is assertable.",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "Behavioral model",
                "sec_num": "3.2"
            },
            {
                "text": "We now turn to a quantitative assessment of the threshold model of response, having addressed two ways in which the unenriched S 1 representation would fail to qualitatively capture behavioral patterns in Jasbi et al (2019)'s TVJT study. Additionally, following Jasbi et al., we recognize that if threshold values were made to be completely invariant across trials of the experiment, then the model would make the undesirable prediction that every participant should have exactly the same response in a given trial type. To allow for population-level variation, the model responder makes a response by comparing the speaker probability against thresholds that are generated from sampling from Gaussian distributions. We thus allow for both population-level and individual level-variation, on the assumption that this sampling procedure takes place whenever a participant is asked to evaluate an utterance in the TVJT. 8 In order to evaluate the RSA-based threshold model, we conducted a Bayesian data analysis. This allowed us to simultaneously generate model predictions and infer likely parameter values, by conditioning on the TVJT data from Jasbi et al. (separately for each of the four responseoption conditions of the experiment) and integrating over the free parameters. Each model assumes uniform priors over utterances and world states as above. We infer the Gaussian threshold distribution parameters and alpha optimality parameters from uniform priors over parameter values using MCMC sampling (observing -for every sample of possible parameter values the expected proportion of responses in that trial type and comparing that distribution to the empirically-observed pattern of response). 9 Additionally, for the Quaterative guess dog, we also assign some probability to dog as a guess in this context -albeit lower probability than is assigned to the conjunctive guess cat and dog.",
                "cite_spans": [
                    {
                        "start": 912,
                        "end": 919,
                        "text": "TVJT. 8",
                        "ref_id": null
                    }
                ],
                "ref_spans": [],
                "eq_spans": [],
                "section": "Quantitative model evaluation",
                "sec_num": "3.3"
            },
            {
                "text": "8 We also introduce a random noise term in the parameter estimation such that the simulated responder makes random guesses on 1% of trials. This noise term is removed when running the model forward to make predictive estimations. 9 We used WebPPL (Goodman and Stuhlm\u00fcller, 2014) for Table 3 : MAP estimates obtained from Bayesian data analysis, where \u21b5 is the optimality parameter, and \u00b5 are Gaussian threshold distribution parameters, and P T is the probability with which the speaker samples from P S P T rather than directly from P S1 . nary and Quinary conditions, we infer from a uniform prior the probability with which the speaker samples from P S P T after sampling from P S 1 . The intuition for restricting the 'Partial Truth' manipulation to these conditions is that the behavioral patterns which this manipulation is intended to cover are only observed in these conditions. 10 Posterior distributions over the parameter values are displayed in Figure 3 , and model predictions using maximum a posteriori (MAP) estimates of the parameter values (Table 3) are plotted against Jasbi et al. (2019)'s results in Figure 1 . Qualitatively, the model addresses each of the desiderata for an empirically adequate linking function discussed above. In all conditions, the model makes predictions for the full range of response options available to participants -thus addressing the issue of intermediate judgments. At the same time, the model addresses the issue of population-level variation: sampling threshold values from Gaussian distributions allows different judgments in the population for a given utterance (while keeping the speaker production probability of that utterance constant).",
                "cite_spans": [
                    {
                        "start": 230,
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                ],
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                    {
                        "start": 283,
                        "end": 290,
                        "text": "Table 3",
                        "ref_id": null
                    },
                    {
                        "start": 956,
                        "end": 964,
                        "text": "Figure 3",
                        "ref_id": null
                    },
                    {
                        "start": 1056,
                        "end": 1065,
                        "text": "(Table 3)",
                        "ref_id": null
                    },
                    {
                        "start": 1119,
                        "end": 1127,
                        "text": "Figure 1",
                        "ref_id": "FIGREF0"
                    }
                ],
                "eq_spans": [],
                "section": "Quantitative model evaluation",
                "sec_num": "3.3"
            },
            {
                "text": "Recall that in the Quaternary and Quinary conditions, there was an asymmetry in the judgment of underinformative disjunctions versus underin-MCMC inference, with 5000 samples (plus a lag of 10 iterations between samples) and a burn-in time of 20,000 iterations. We computed maximum a posteriori values from the marginal posterior distributions over parameter values using the density function in R. 10 We speculate that there may be a link between increasing the number of response options and participants' increased expectation of Partial Truth speaker behavior, which may have been strengthened by the fact that the Quaternary and Quinary conditions explicitly made reference to gradient levels of correctness (i.e. 'Kinda Right' / 'Kinda Wrong'). But this speculation warrants future investigation. formative simple declaratives. The model makes use of the 'Partial Truth' speaker function in order to adjust the underlying speaker production probabilities -and hence the distribution of predicted response options -for these utterances. The 'Partial Truth' function also boosts the production probability of strictly false conjunctions, allowing the model to predict responses other than 'Wrong' for this trial type. Thus, the 'Partial Truth' enrichment helps to address both scalar diversity and endorsement of false utterances. 11 The correlation between empirical observations and model predictions is high (Adj. R 2 > 0.9 in all conditions), suggesting that the threshold responder model is a good model of TVJT behavior overall. Nevertheless, the model makes some undesirable predictions. For example, it over-predicts rates of 'Neither' responses in the Quinary condition. Empirically, this response tended to be disfavored relative to positive and negative response options, for example in the case of strictly false cat and dog guesses. The model assumes that the labeling of the response options should have no particular effect on selection, but future work should engage with this assumption.",
                "cite_spans": [
                    {
                        "start": 399,
                        "end": 401,
                        "text": "10",
                        "ref_id": null
                    },
                    {
                        "start": 1335,
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                        "text": "11",
                        "ref_id": null
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                ],
                "ref_spans": [],
                "eq_spans": [],
                "section": "Quantitative model evaluation",
                "sec_num": "3.3"
            },
            {
                "text": "Based on a single underlying probabilistic model of pragmatic competence, the presented threshold responder model provides a level of empirical coverage for TVJT data unavailable to existing linking models rooted in the categorical view of scalar implicature. The contribution of this paper is twofold: methodologically, we present this analysis as a proof-of-concept approach to modeling TVJT data for researchers in experimental semantics/pragmatics. We see the presented behavioral model as a starting point for future quantitative analytic work in the TVJT domain -a model against which future models may be assessed. 12 On the theoretical side, the cognitive model that forms the basis for the behavioral model is nonneutral in its assumptions. In particular, it assumes that TVJT behavior is the result of reasoning about probabilistic utterance choices that Figure 3 : Normalized marginal posterior distributions over parameter values for the threshold responder model in each experimental condition. Note that the posterior distribution for the optimality parameter \u21b5 has been rescaled for the purposes of this visualization.",
                "cite_spans": [
                    {
                        "start": 622,
                        "end": 624,
                        "text": "12",
                        "ref_id": null
                    }
                ],
                "ref_spans": [
                    {
                        "start": 865,
                        "end": 873,
                        "text": "Figure 3",
                        "ref_id": null
                    }
                ],
                "eq_spans": [],
                "section": "Discussion and Conclusion",
                "sec_num": "4"
            },
            {
                "text": "are the result of trading off (contextual) utterance informativeness and cost. Under this view, not only does TVJT behavior not quantify implicature rates; the very notion of an implicature evaporates. Rather than finding this undesirable, we believe that this framework allows for more rigorous engagement with the complexities of linking theoretical constructs to behavior (see also Franke 2016), an area of some dearth in experimental semantics/pragmatics. -",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "Discussion and Conclusion",
                "sec_num": "4"
            },
            {
                "text": "Data and code for all analyses and graphs are available at http://github.com/bwaldon/tvjt_linking.",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "",
                "sec_num": null
            },
            {
                "text": "Following Degen and Goodman (2014), the authors argue that conceptually, behavior on TVJTs is better modeled as a function of an agent's representation of a pragmatic speaker rather than of a pragmatic listener.",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "",
                "sec_num": null
            },
            {
                "text": "We include dog as a possible guess because we posit that participants have no reason a priori to expect the other true and underinformative simple declarativecat -over this equally informative guess in two-animal card conditions.",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "",
                "sec_num": null
            },
            {
                "text": "For our implementation of SPT , we restrict the distribution such that u 0 must entail (or be entailed by) u in order to have probability above 0. Without this restriction, SPT could in principle assign high probability to utterances which have no relevance to the question under discussion (i.e. \"What animals are on the card?\"), by virtue of those utterances' assertability in worlds consistent with u. A systematic exploration of the linguistic alternatives available to S1 (as well as SPT ) is a question we must leave to future work.",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "",
                "sec_num": null
            },
            {
                "text": "We leave further investigation of the 'Partial Truth' function -in particular its extension to an analysis of linguistic imprecision as sketched above -to future work.12 For example, one could in principle link the threshold model to pragmatic listener probabilities of meanings given utterances rather than to speaker production probabilities given intended meanings (as we do in this paper).",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "",
                "sec_num": null
            }
        ],
        "back_matter": [],
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        "ref_entries": {
            "FIGREF0": {
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                "uris": null,
                "text": "Model predictions (light bars) plotted against empirical results (dark bars) from Jasbi et al.'s (2019) TVJT study. Error bars indicate 95% multinomial confidence intervals. Red and green bars indicate false and true trials, respectively; blue bars indicate implicature trials.",
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            "TABREF0": {
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                "content": "<table><tr><td>:</td><td>Response-option conditions of Jasbi et</td></tr><tr><td colspan=\"2\">al. (2019)'s TVJT study.</td></tr></table>",
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            "TABREF1": {
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                "text": "Cards used in Jasbi et al. (2019)'s TVJT.",
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    }
}