Free Choice Inferences Research Articles

Russian Disjunction To li To li and Obligatory Ignorance

Abstract In this paper, we explore the behavior of one complex disjunction in Russian that has some special properties that set it apart from other simple and complex disjunctions: it never gives rise to free choice inferences in environments in which other disjunctions do and under universal quantifiers it behaves different from other disjunctions. We show that the data resist an analysis in terms of wide scope disjunction and propose that those special properties are due to obligatory ignorance inferences associated with this disjunction. The paper provides one more argument for a grammatical theory of ignorance along the lines of ( 7).

Logic and conversation: The case of free choice

Free choice inferences represent a much discussed case of a divergence between logic and language (Kamp 1973, Zimmermann 2000). Grice influentially argued that the assumption that such divergence does in fact exist is a mistake originating “from inadequate attention to the nature and importance of the conditions governing conversation” (Grice 1989: 24). I will first show that when applied to free choice phenomena, the standard implementation of Grice’s view, representing semantics and pragmatics as two separate components, is empirically inadequate. I will then propose a different account: a bilateral state-based modal logic modelling next to literal meanings also pragmatic factors and the additional inferences that arise from their interaction. The pragmatic factor I will consider connects to a tendency of language users to neglect empty configurations when engaging in linguistic interpretation. The non-emptiness atom (ne) from team semantics provides a perspicuous way to formally represent this tendency and to rigorously study its impact on interpretation. In terms of ne, I will define a pragmatic enrichment function and show that, in interaction with disjunction occurring in positive contexts and only in these cases, pragmatic enrichment yields non-trivial effects including predicting free choice inferences and their cancellation under negation. The latter result relies on the adopted bilateralism, where each connective comes with an assertion and a rejection condition and negation is defined in terms of the latter notion. EARLY ACCESS

Remarks on disjunctive focus-associates

This paper concerns similarities and differences between the implicatures of dis-junction — modalized disjunction specifically — and the implicatures of other scalar terms like some. The two inference types are compared with special attention to their behavior under association with only, where they are shown to come apart. I argue that disjunct alternatives (p,q) to a disjunctive associate of only ([p or q]) do not feed the semantics of the particle. The significance of the claim is discussed in connection to (a) semantic and implicature-based accounts of free choice inferences, and (b) the phenomenon of presupposed implicatures.

Indefinites and free choice

Indefinites display a great functional variety and they give rise to different pragmatic effects. We focus on free choice indefinites and in particular on the Italian qualsiasi. Our aim is to reconstruct the grammaticalization path of this item and understand how diachronic data might shed some light on existing semantic theories of free choice. We employ corpus-based tools to build a database containing occurrences of qualsiasi from its origin and early forms to its current usage. We show that qualsiasi emerged from a particular unconditional construction and we outline the different stages which led to its grammaticalization. We analyze the compatibility of our diachronic study with formal accounts of free choice inferences, with a focus on Alternative Semantics analyses for indefinite pronouns and so-called grammatical theories of free choice. Our work shows that an integration between formal semantics and historical linguistics is fruitful and worth pursuing.

Presupposed free choice and the theory of scalar implicatures

A disjunctive sentence like Olivia took Logic or Algebra conveys that Olivia didn’t take both classes (exclusivity) and that the speaker doesn’t know which of the two classes she took (ignorance). The corresponding sentence with a possibility modal, Olivia can take Logic or Algebra, conveys instead that she can take Logic and that she can take Algebra (free choice). These exclusivity, ignorance and free choice inferences are argued by many to be scalar implicatures. Recent work has looked at cases in which exclusivity and ignorance appear to be computed instead at the presupposition level, independently from the assertion. On the basis of those data, Spector and Sudo (Linguist Philos 40(5):473–517, 2017) have argued for a hybrid account relying on a pragmatic principle for deriving implicatures in the presupposition. In this paper, we observe that a sentence like Noah is unaware that Olivia can take Logic or Algebra has a reading on which free choice appears in the presupposition, but not in the assertion, and we show that deriving this reading is challenging on Spector and Sudo’s (2017) hybrid account. Following the dialectic in Fox (Presupposition and implicature in compositional semantics, Palgrave, London, pp 71–120, 2007), we argue against a pragmatic approach to presupposition-based implicatures on the ground that it is not able to account for presupposed free choice. In addition, we raise a novel challenge for Spector and Sudo’s (2017) account coming from the conflicting presupposed ignorance triggered by sentences like #Noah is unaware that I have a son or a daughter, which is infelicitous even if it’s not common knowledge whether the speaker has a son or a daughter. More generally, our data reveals a systematic parallelism between the assertion and presupposition levels in terms of exclusivity, ignorance, and free choice. We argue that such parallels call for a unified analysis and we sketch how a grammatical theory of implicatures where meaning strengthening operates in a similar way at both levels (Gajewski and Sharvit in Nat Lang Semant 20(1):31–57, 2012; Magri in A theory of individual-level predicates based on blind mandatory scalar implicatures, MIT dissertation, 2009; Marty in Implicatures in the DP domain, MIT dissertation, 2017) can account for such parallels.

Negation and Free Choice Inference in Child Mandarin.

In sentences with internal negation, Free Choice Inferences (FCIs) are canceled (Chierchia, 2013). The present study investigated the possibility that FCIs are negated, not canceled, by external negation. In previous research, both Mandarin-speaking children and adults were found to license FCIs in affirmative sentences with a modal verb and the disjunction word huozhe ‘or’ (Zhou et al., 2013). The present study contrasted internal versus external negation in sentences that contained all the ingredients needed to license FCIs. Four experiments were conducted using the Truth Value Judgment Task (Crain and Thornton, 1998). Experiment 1 tested Mandarin-speaking children and adults using sentences with internal negation, a modal verb and disjunction. As expected, children did not license FCIs; rather, they assigned a ‘neither’ interpretation to disjunction. Also as expected, adults analyzed disjunction as taking scope over internal negation, yielding a ‘not both’ interpretation (Jing et al., 2005). Experiment 1 provided the benchmarks for sentences with external negation in Experiments 2-4. Experiment 2 confirmed that English-speaking adults distinguish between internal and external negation in sentences with disjunction. In Experiment 3, external negation was conveyed by the focus adverb zhiyou ‘only’. External negation eliminated the between-group differences observed in Experiment 1. Both children and adults analyzed external negation as taking scope over disjunction. Experiment 4 tested the effect of external negation on the computation of FCIs. The test sentences only differed from Experiment 1 by using external negation, rather than internal negation. Again, children and adults interpreted the test sentences in the same way. Most importantly, in contrast to Experiment 1 (with internal negation), both groups analyzed external negation as negating, rather than canceling, FCIs. The findings support the distinction between internal and external negation.

A TWO-DIMENSIONAL LOGIC FOR TWO PARADOXES OF DEONTIC MODALITY

AbstractIn this paper, we axiomatize the deontic logic in Fusco (2015), which uses a Stalnaker-inspired account of diagonal acceptance and a two-dimensional account of disjunction to treat Ross’s Paradox and the Puzzle of Free Choice Permission. On this account, disjunction-involving validities are a priori rather than necessary. We show how to axiomatize two-dimensional disjunction so that the introduction/elimination rules for boolean disjunction can be viewed as one-dimensional projections of more general two-dimensional rules. These completeness results help make explicit the restrictions Fusco’s account must place on free-choice inferences. They are also of independent interest, as they raise difficult questions about how to “lift” a Kripke frame for a one-dimensional modal logic into two dimensions.

Agential Free Choice

The Free Choice effect—whereby $\lozenge (p {\textsc {or}} q)$ seems to entail both $\lozenge p$ and $\lozenge q$ —has traditionally been characterized as a phenomenon affecting the deontic modal ‘may’. This paper presents an extension of the semantic account of free choice defended by Fusco (Philosophers’ Imprint, 15, 1–27, 2015) to the agentive modal ‘can’, the ‘can’ which, intuitively, describes an agent’s powers. On this account, free choice is a nonspecific de re phenomenon (Bauerle 1983; Fodor 1970) that—unlike typical cases—affects disjunction. I begin by sketching a model of inexact ability, which grounds a modal approach to agency (Belnap Theoria, 54, 175–199, 1998; Perloff 2001) in a Williamson (Mind, 101, 217–242, 1992; Erkenntnis, 79, 971–999, 2014)-style margin of error. A classical propositional semantics combined with this framework can reflect the intuitions highlighted by Kenny (1976)’s dartboard cases, as well as the counterexamples to simple conditional views recently discussed by Mandelkern et al. (Philosophical Review, 126, 301–343, 2017). In Section 3, I turn to an independently motivated actual-world-sensitive account of disjunction, and show how it extends free choice inferences into an object language for propositional modal logic.

Free choice effects and exclusive disjunction

ABSTRACT This paper presents experimental data relevant to understanding the modal free choice effect (Kamp, 1973) when there are more than two disjuncts under the relevant modal operator. The results suggest that speakers' willingness to draw free choice inferences is correlated with whether the embedded disjuncts are modally separable, in a sense brought into focus by considering cases within which the relevant propositions fail to be pairwise redundant but are redundant as a set.

Two puzzles about ability can

The received wisdom on ability modals is that they differ from their epistemic and deontic cousins in what inferences they license and better receive a universal or conditional analysis instead of an existential one. The goal of this paper is to sharpen the empirical picture about the semantics of ability modals, and to propose an analysis that explains what makes the can of ability so special but that also preserves the crucial idea that all uses of can share a common lexical semantics. The resulting framework combines tools and techniques from dynamic and inquisitive semantics with insights from the literature of the role of agency in deontic logic. It explains not only why the can of ability, while essentially being an existential modal operator, sometimes resists distribution over disjunction and interacts with its duals in particular and hitherto unnoticed ways, but also has a tendency to license free choice inferences.

Context, Content, and the Occasional Costs of Implicature Computation.

The computation of scalar implicatures is sometimes costly relative to basic meanings. Among the costly computations are those that involve strengthening “some” to “not all” and strengthening inclusive disjunction to exclusive disjunction. The opposite is true for some other cases of strengthening, where the strengthened meaning is less costly than its corresponding basic meaning. These include conjunctive strengthenings of disjunctive sentences (e.g., free-choice inferences) and exactly-readings of numerals. Assuming that these are indeed all instances of strengthening via implicature/exhaustification, the puzzle is to explain why strengthening sometimes increases costs while at other times it decreases costs. I develop a theory of processing costs that makes no reference to the strengthening mechanism or to other aspects of the derivation of the sentence's form/meaning. Instead, costs are determined by domain-general considerations of the grammar's output, and in particular by aspects of the meanings of ambiguous sentences and particular ways they update the context. Specifically, I propose that when the hearer has to disambiguate between a sentence's basic and strengthened meaning, the processing cost of any particular choice is a function of (i) a measure of the semantic complexity of the chosen meaning and (ii) a measure of how much relevant uncertainty it leaves behind in the context. I measure semantic complexity with Boolean Complexity in the propositional case and with semantic automata in the quantificational case, both of which give a domain-general measure of the minimal representational complexity needed to express the given meaning. I measure relevant uncertainty with the information-theoretic notion of entropy; this domain-general measure formalizes how ‘far' the meaning is from giving a complete answer to the question under discussion, and hence gives an indication of how much representational complexity is yet to come. Processing costs thus follow from domain-general considerations of current and anticipated representational complexity. The results might also speak to functional motivations for having strengthening mechanisms in the first place. Specifically, exhaustification allows language users to use simpler forms than would be available without it to both resolve relevant uncertainties and convey complex meanings.

Free choice and distribution over disjunction: the case of free choice ability

This squib discusses the semantics of ability modals in relation to the law of distribution over disjunction and free choice effects. Most current analyses of free choice need distribution over disjunction as a theorem for modals in order to correctly derive free choice inferences. Famously, however, ability modals have been argued to fail to meet distribution over disjunction (Kenny 1976). The squib explores to what extent free choice abilities are dependent on the distribution property. EARLY ACCESS

Positive polarity indefinites? On how (not) to identify them: An exhaustification-based perspective

Abstract This paper discusses a class of so-called “marked” or “modal” indefinites in Romance, (e.g., Romanian un NP oarecare, Italian un NP qualunque, French quelque N), which have been shown to display the locality, shielding and rescuing effects familiar from the study of positive polarity items (PPIs) like someone (e.g., Săvescu-Ciucivara 2007, Oarecare indefinites are not just any indefinites. In Gabriela Alboiu, Andrei Avram, Larisa Avram & Daniela Isac (eds.), Pitar Moș: A building with a view: Papers in honour of Alexandra Cornilescu, 205–225. Bucharest: Editura Universității din București; Jayez and Tovena 2007, Evidentiality and determination. In Atle Grønn (ed.), Proceedings of Sinn und Bedeutung 12, 271–286. Oslo: Department of Literature, Area Studies and European Languages, University of Oslo; Chierchia 2013, Logic in grammar. Oxford: Oxford University Press). Taking Romanian as a case study, I show that in positive contexts, these indefinites exhibit properties (obligatory non-specificity, free choice inferences) that set them apart from someone-PPIs and make them very similar to free choice indefinites. Adopting the framework in Chierchia (2013), we account for the interpretation of indefinites like un NP oarecare by assuming they activate scalar and domain alternatives. The computation of these alternatives is argued to be responsible for the observed interpretation and interaction with negation (as well as other positive polarity features). The proposed account emphasizes the connection between free choice and positive polarity and suggests that positive polarity behavior stems from more than one source.

Wh-Questions, Universal Statements and Free Choice Inferences in Child Mandarin.

This study investigated 5-year-old Mandarin-speaking children's comprehension of wh-questions, universal statements and free choice inferences. Previous research has found that Mandarin-speaking children assign a universal interpretation to sentences with a wh-word (e.g., shei 'who') followed by the adverbial quantifier dou 'all' (Zhou in Appl Psycholinguist 36:411-435, 2013). Children also compute free choice inferences in sentences that contain a modal verb in addition to a wh-word and dou (Zhou, in: Nakayama, Su, Huang (eds.) Studies in Chinese and Japanese language acquisition: in honour of Stephen Crain. John Benjamins Publishing Company, Amsterdam, pp 223-235, 2017). The present study used a Question-Statement Task to assess children's interpretation of sentences containing shei + dou, both with and without the modal verb beiyunxu 'was allowed to', as well as the contrast between sentences with shei + dou, which are statements for adults, versus ones with dou + shei, which are wh-questions for adults. The 5-year-old Mandarin-speaking child participants exhibited adult-like linguistic knowledge of the semantics and pragmatics of wh-words, the adverbial quantifier dou, and the deontic modal verb beiyunxu.

Universal Free Choice and Innocent Inclusion

The goal of this paper is to provide a global account of universal Free Choice (FC) inferences (argued to be needed in Chemla 2009b). We propose a stronger exhaustivity operator than proposed in Fox (2007), one that doesn’t only negate all the Innocently Excludable (IE) alternatives but also asserts all the ``Innocently Includable'' (II) ones, and subsequently can derive universal FC inferences globally. We further show that Innocent Inclusion is independently motivated by considerations that come from the semantics of only (data from Alxatib 2014). Finally, the distinction between Innocent Exclusion and Innocent Inclusion allows us to capture differences between FC inferences and other scalar implicatures.

Probability and implicatures: A unified account of the scalar effects of disjunction under modals

Sentences involving disjunction under epistemic modal adjectives — such as possible , likely , and certain — give rise to the inference that the disjuncts are epistemically possible. Inferences of this sort are often classified and treated differently, depending on the force of the embedding modal. Those triggered by possibility modals are singled out as ‘free choice inferences’ (Kratzer & Shimoyama 2002, Klinedinst 2007, Fox 2007, Chierchia 2013, a.o.), while those triggered by stronger modals are called and accounted for in a different way (Sauerland 2004, Fox 2007, Crnic et al. 2015 a.o.). In this paper, we pursue two goals. First, we develop and defend a degree semantics for epistemic modal adjectives, building on much recent work on the topic (Yalcin 2010, Lassiter 2011, 2014, Moss 2015, Swanson 2015, a.o.). Second, we show that this semantics, in combination with the assumption that scalar implicatures can arise in embedded position (Fox 2007, Chierchia et al. 2012 a.o.), can predict all the inferences triggered by disjunction under modals, including free choice ones, via a uniform mechanism. We conclude by outlining how the proposal can be extended to epistemic modal items in other syntactic categories, and to modals of different flavor. BibTeX Info

Free Choice under Ellipsis

AbstractThe ellipsis of a VP whose antecedent contains an occurrence of so-called free choiceanyis highly constrained: it is acceptable only if the elided VP is appropriately embedded. We show that while this is unexpected on the common approaches to free choice and ellipsis, it is predicted on a theory ofanythat takes its domain to stand in a dependency relation with a c-commanding alternative-sensitive operator (cf. Lahiri 1998, Focus and negative polarity in Hindi.Natural Language Semantics6(1). 57–123) and that takes free choice inferences to be generated by covert exhaustification in grammar (e.g., Fox 2007, Free choice and the theory of scalar implicatures. In Uli Sauerland & Penka Stateva (eds.),Presupposition and implicature in compositional semantics, 71–120. Palgrave Macmillan; Chierchia 2013,Logic in grammar. Oxford: Oxford University Press).

Actuality Entailments, negation, and free choice inferences

In some languages, (certain) root modals license Actuality Entailments (AEs) when they are perfective-marked. We discuss two puzzling properties of these constructions: (i) when AE-licensing modals are negated, the result entails the negation of actuality, and (ii) when AE-licensing modals embed disjunctions, no Free Choice inferences are available. We develop an account of (i) and show that, given an implicature-based view of Free Choice, (ii) follows as a consequence.

Processing Conversational Implicatures: Alternatives and Counterfactual Reasoning.

In a series of experiments, Bott and Noveck (2004) found that the computation of scalar inferences, a variety of conversational implicature, caused a delay in response times. In order to determine what aspect of the inferential process that underlies scalar inferences caused this delay, we extended their paradigm to three other kinds of inferences: free choice inferences, conditional perfection, and exhaustivity in "it"-clefts. In contrast to scalar inferences, the computation of these three kinds of inferences facilitated response times. Following a suggestion made by Chemla and Bott (2014), we propose that the time it takes to compute a conversational implicature depends on the structural characteristics of the required alternatives.

Children's knowledge of free choice inferences

This paper presents experimental results showing that four-year-old Mandarin- speaking children draw free choice inferences from disjunctive statements, though they are not able to compute inferences of exclusivity for disjunctive statements or other scalar implicatures. The findings connect to those of Chemla & Bott (under review) who report differences in how adults process free choice inferences versus scalar implicatures and, prima facie, the findings pose a challenge to treatments that attempt to unify inferences of both kinds. Instead, the findings appear to favour accounts that invoke different analyses for each kind of inference, such as Zimmerman 2000a, Geurts 2005, and Barker 2010. The results, however, also support the recent approach in the experimental literature which attributes children’s failures to compute scalar implicatures to a difficulty with alternatives: children may lack the lexical knowledge of alternatives, or these implicatures impose such a high processing cost that children are unable to handle the alternatives necessary to compute them (Gualmini, Crain, Meroni, Chierchia & Guasti 2001 Chierchia, Crain, Guasti & Thornton 2001 Reinhart 2006; Barner, Brooks & Bale 2011; Singh, Wexler, Astle, Kamawar & Fox 2012). If accessing alternatives is the source of children’s difficulty, then they would be expected to perform better if the requisite alternatives are made explicit, as sub-strings of the asserted sentences. This is exactly what we found. Children were able to compute free choice inferences based on alternatives that were made explicit in the assertion, but children were unable to compute ‘regular’ scalar implicatures arising from alternatives lacking this property. We discuss the implications of these findings for the debate about the relationship between free choice inferences and scalar implicatures and children’s knowledge of alternatives.