The minimal weakening \ of Belnap-Dunn logic under the polarity semantics for negation as a modal operator is formulated as a sequent system which is characterized by the class of all birelational frames. Some extensions of \ with additional sequents as axioms are introduced. In particular, all three modal negation logics characterized by a frame with a single state are formalized as extensions of \. These logics have the finite model property and they are decidable.

Epistemic modal verbs and adverbs of necessity are claimed to be positive polarity items. We study their behavior by examining modal spread, a phenomenon that appears redundant or even anomalous, since it involves two apparent modal operators being interpreted as a single modality. We propose an analysis in which the modal adverb is an argument of the MUST modal, providing a meta-evaluation \ which ranks the Ideal, stereotypical worlds in the modal base as better possibilities than the Non-Ideal worlds (...) in it. MUST and possibility modals differ in that the latter have an empty \, a default that can be negotiated. Languages vary in the malleability of this parameter. Positive polarity is derived as a conflict between the ranking imposed by \—which requires that the Ideal worlds be better possibilities than Non-Ideal worlds—and the effect of higher negation which renders the Ideal set non-homogenous. Applying the ordering over such a non-homogeneous set would express preference towards both p and \ worlds thus rendering the sentence uninformative. Negative polarity MUST and possibility modals, on the other hand, contain an empty \, application of higher negation therefore poses no problem. This account is the first to connect modal spread to positive polarity of necessity modals, and captures the properties of both in a unified analysis. (shrink)

This paper presents a polarized phase semantics, with respect to which the linear fragment of second order polarized linear logic of Laurent [15] is complete. This is done by adding a topological structure to Girard's phase semantics [9]. The topological structure results naturally from the categorical construction developed by Hamano—Scott [12]. The polarity shifting operator ↓ (resp. ↑) is interpreted as an interior (resp. closure) operator in such a manner that positive (resp. negative) formulas correspond to open (resp. closed) (...) facts. By accommodating the exponentials of linear logic, our model is extended to the polarized fragment of the second order linear logic. Strong forms of completeness theorems are given to yield cut-eliminations for the both second order systems. As an application of our semantics, the first order conservativity of linear logic is studied over its polarized fragment of Laurent [16]. Using a counter model construction, the extension of this conservativity is shown to fail into the second order, whose solution is posed as an open problem in [16]. After this negative result, a second order conservativity theorem is proved for an eta expanded fragment of the second order linear logic, which fragment retains a focalized sequent property of [3]. (shrink)

We model the conventional meaning of utterances that combine two distinct clause types: a (positive) declarative or imperative (in rare cases, interrogative) anchor and a (negative) interrogative tag, such as won’t you?. We argue that such utterances express a single speech act, and in fact, a single conventional update of the conversational scoreboard. The proposed model of this effect is a straightforward extension of prior proposals for the semantics of declaratives, imperatives, and preposed-negation interrogatives. Ours is the first unified account (...) of these phenomena that addresses the sentential force of these utterances and outlines how the speech act effects arise from the scoreboard update and contextual factors. We enrich the conversational scoreboard, interpreted as a model of sentential force, to include graded commitments and non-at-issue meanings. A consequence of our model is that modified utterances can create “blended” speech acts which share some, but not all, properties with the unmodified utterances. The proposal has implications for models of other utterance modifiers, as well as for negative interrogatives and negation in general, and for imperative/jussive constructions. (shrink)

In this paper, we present a categorical model for Multiplicative Additive Polarized Linear Logic , which is the linear fragment of Olivier Laurent’s Polarized Linear Logic. Our model is based on an adjunction between reflective/coreflective full subcategories / of an ambient *-autonomous category . Similar structures were first introduced by M. Barr in the late 1970’s in abstract duality theory and more recently in work on game semantics for linear logic. The paper has two goals: to discuss concrete models and (...) to present various completeness theorems.As concrete examples, we present a hypercoherence model, using Ehrhard’s hereditary/anti-hereditary objects, a Chu-space model, a double gluing model over our categorical framework, and a model based on iterated double gluing over a *-autonomous category.For the multiplicative fragment of. (shrink)

Linguists often sharply distinguish the different modules that support linguistics competence, e.g., syntax, semantics, pragmatics. However, recent work has identified phenomena in syntax (polarity sensitivity) and pragmatics (implicatures), which seem to rely on semantic properties (monotonicity). We propose to investigate these phenomena and their connections as a window into the modularity of our linguistic knowledge. We conducted a series of experiments to gather the relevant syntactic, semantic and pragmatic judgments within a single paradigm. The comparison between these (...) quantitative data leads us to four main results, (i) Our results support a departure from one element of the classical Gricean approach, thus helping to clarify and settle an empirical debate. This first outcome also confirms the soundness of the methodology, as the results align with standard contemporary accounts of scalar implicature (SI), (ii) We confirm that the formal semantic notion of monotonicity underlies negative polarity item (NPI) syntactic acceptability, but (iii) our results indicate that the notion needed is perceived monotonicity. We see results (ii) and (iii) as the main contribution of this study: (ii) provides an empirical interpretation and confirmation of one of the insights of the model-theoretic approach to semantics, while (iii) calls for an incremental, cognitive implementation of the current generalizations, (iv) Finally, our results do not indicate that the relationship between NPI acceptability and monotonicity is mediated by pragmatic features related to Sis: this tells against elegant attempts to unify polarity sensitivity and Sis (pioneered by Krifka and Chierchia). These results illustrate a new methodology for integrating theoretically rigorous work in formal semantics with an experimentally-grounded cognitively-oriented view of linguistic competence. (shrink)

Semantic information is usually supposed to satisfy the veridicality thesis: p qualifies as semantic information only if p is true. However, what it means for semantic information to be true is often left implicit, with correspondentist interpretations representing the most popular, default option. The article develops an alternative approach, namely a correctness theory of truth (CTT) for semantic information. This is meant as a contribution not only to the philosophy of information but also to the philosophical (...) debate on the nature of truth. After the introduction, in Sect. 2, semantic information is shown to be translatable into propositional semantic information (i). In Sect. 3, i is polarised into a query (Q) and a result (R), qualified by a specific context, a level of abstraction and a purpose. This polarization is normalised in Sect. 4, where [Q + R] is transformed into a Boolean question and its relative yes/no answer [Q + A]. This completes the reduction of the truth of i to the correctness of A. In Sects. 5 and 6, it is argued that (1) A is the correct answer to Q if and only if (2) A correctly saturates Q by verifying and validating it (in the computer science’s sense of “verification” and “validation”); that (2) is the case if and only if (3) [Q + A] generates an adequate model (m) of the relevant system (s) identified by Q; that (3) is the case if and only if (4) m is a proxy of s (in the computer science’s sense of “proxy”) and (5) proximal access to m commutes with the distal access to s (in the category theory’s sense of “commutation”); and that (5) is the case if and only if (6) reading/writing (accessing, in the computer science’s technical sense of the term) m enables one to read/write (access) s. Sect. 7 provides some further clarifications about CTT, in the light of semantic paradoxes. Section 8 draws a general conclusion about the nature of CTT as a theory for systems designers not just systems users. In the course of the article all technical expressions from computer science are explained. (shrink)

In this paper, I examine the syntax-semantics of subjunctive clauses in (Modern) Greek. These clauses are headed by the particle na and contain a dependent verbal form with no formal mood features: the perfective nonpast (PNP). I propose that the semantics of na is temporal: it introduces the variable now (n) into the syntax. This is necessary because the apparent present tense in the PNP cannot introduce n. The PNP, instead, contains a dependent time variable. This variable cannot be interpreted (...) as a free variable – hence it cannot be identified with the utterance time of the context. This analysis relies on two premises. One is the (quite influential) idea that pronouns and tenses are analogous creatures (Partee 1973, 1984, Heim 1998, Kratzer 1998, and others). The other premise is that at least some polarity items are expressions that contain variables that cannot be interpreted deictically (Giannakidou 1998, 2001). In the present work I suggest to enlarge the domain of phenomena that can receive a unified treatment across individuals, worlds, and tenses, and treat the subjunctive mood as a non-deictic time, thus an instance of a polarity dependency of the temporal kind. It is my hope that the analysis proposed here for the PNP can be used to analyze verbal subjunctives in Romance languages, and perhaps also infinitival forms in English, but investigation of this question will have be left for the future. (shrink)

Positive polarity items (PPIs) are generally thought to have the boring property that they cannot scope below negation. The starting point of the paper is the observation that their distribution is significantly more complex; specifically, someone/something-type PPIs share properties with negative polarity items (NPIs). First, these PPIs are disallowed in the same environments that license yet type NPIs; second, adding any NPI-licenser rescues the illegitimate constellation. This leads to the conclusion that these PPIs have the combined properties of (...) yet-type and ever-type NPIs: what appears to be a prohibition is nothing but “halfway licensing”. The paper goes on to propose a unification of the analyses of rescuable PPIs, NPIs, and negative concord, and questions the grounding of polarity sensitivity in the scalar or the referential semantics of the items involved. (shrink)

This paper uses the distribution and interpretation of antonymous adjectives in comparative constructions as an empirical basis to argue that abstract representations of measurement, or ‘degrees’, must be modeled as intervals on a scale, rather than as points, as commonly assumed. I begin by demonstrating that the facts in this domain must be accounted for in terms of the interaction of the semantics of adjectival polarity and the semantics of the comparative, rather than principles governing the (overt) expression of (...) particular types of adjectives in comparatives. I then show that a principled account of the full range of data under consideration can be constructed within a model in which degrees are formalized as intervals on a scale and adjectival polarity is characterized in terms of two structurally distinct and complementary sorts of `positive' and `negative' degrees. (shrink)

An electronic poster from "Polarity from Different Perspectives," New York University, 2005. The authors present an experiment that investigated to what extent six negative polarity items (slept a wink, in ages, ever, much, at all, and yet) are licensed by 9 potential licensers.

In this paper, we propose an analysis of metalinguistic comparatives (MCs) in Greek and Korean which combines an attitudinal semantics (Giannakidou and Stavrou 2008) with an expressive component. The comparative morpheme supplies the former, and the than-particle supplies the latter. Following Giannakidou and Stavrou, we assume that the MC involves the speaker’s attitude towards the than-proposition— which is deemed less appropriate or preferable— and we discuss novel data from Korean showing a two way distinction between “regular” MCs (signaled by the (...) particle kipota), and negative MCs (signaled by charari “rather” and the particle nuni). We argue that the use of MC than particles, in all variants, brings about an individual’s emotive state, and propose that the morphemes contain expressive indices in the sense of Potts 2007. Indices allow a range from mildly negative to very negative stance, so we capture the fact that expressive particles convey negativity, without positing negation in syntax— a result consistent with the fact that MC-than itself does not license strong NPIs that need negation. We further show that NPI sanctioning in comparatives is very limited, contrary to what is generally thought. Besides NPI-sanctioning, this analysis has two, we believe, important implications. First, it allows the generalization that metalinguistic functions in language are indeed part of the grammar as a combination of attitude semantics and expressivity. Additionally, our use of expressive indices supports Potts’s view of the expressive component as separate, but interacting, with the descriptive content. Finally, we show that the than particle is not vacuous (as is generally believed) but contentful: it is the locus of the interaction between descriptive and expressive meaning in the comparative. (shrink)

The present paper is an attempt at the investigation of the nature of polarity contrast in natural languages. Truth conditions for natural language sentences are incomplete unless they include a proper definition of the conditions under which they are false. It is argued that the tertium non datur principle of classical bivalent logical systems is empirically invalid for natural languages: falsity cannot be equated with non-truth. Lacking a direct intuition about the conditions under which a sentence is false, we (...) need an independent foundation of the concept of falsity. The solution I offer is a definition of falsity in terms of the truth of a syntactic negation of the sentence. A definition of syntactic negation is proposed for English. (shrink)

This paper takes a stand on Hamblin semantics and its relation to the semantics-to-pragmatics interface. Biased questions, where the speaker finds one of the options more likely and expects the confirmation that p is true, raise a concern about the limits of Hamblin semantics. I argue that biased questions have modified Hamblin semantics, while unbiased questions have unconstrained Hamblin semantics. The optional bias feature explains compositionally. It is triggered by likelihood presuppositions ranging Hamblin sets and highlighting the preferred alternative(s). Biased (...) effects are exceptionally possible in alternative and wh-questions, but only in polar questions, they can be encoded lexically and grammatically. I argue that Hamblin semantics covers all core types of questions, while some of its applications for non-questions are problematic. (shrink)

This volume offers insights on experimental and empirical research in theoretical linguistic issues of negation and polarity, focusing on how negation is marked and how negative polarity is emphatic and how it interacts with double negation. Metalinguistic negation and neg-raising are also explored in the volume. Leading specialists in the field present novel ideas by employing various experimental methods in felicity judgments, eye tracking, self-paced readings, prosody and ERP. Particular attention is given to extensive crosslinguistc data from French, (...) Catalan and Korean along with analyses using semantic and pragmatic methods, corpus linguistics, diachronic perspectives, and longitudinal acquisitional studies as well as signed and gestural negation. Each contribution is situated with regards to major previous studies, thereby offering readers insights on the current state of the art in research on negation and negative polarity, highlighting how theory and data together contributes to the understanding of cognition and mind.. (shrink)

This paper gives an account of the differences between polar and alternative questions, as well as an account of the division of labor between compositional semantics and pragmatics in interpreting these types of questions. Alternative questions involve a strong exhaustivity presupposition for the mentioned alternatives. We derive this compositionally from the meaning of the final falling tone and its interaction with the pragmatics of questioning in discourse. Alternative questions are exhaustive in two ways: they exhaust the space of epistemic possibilities, (...) as well as the space of discourse possibilities (the Question Under Discussion). In contrast, we propose that polar questions are the opposite: they present just one alternative that is necessarily non-exhaustive. The account explains a range of response patterns to alternative and polar questions, as well as differences and similarities between the two types of questions. (shrink)

Negative polarity is one of the more elusive aspects of linguistics and a subject which has been gaining in importance in recent years. Written from within the well-defined theoretical framework of Generalized Quantifiers, the three main areas considered in this study are collocations, polarity items and multiple negations. In this mature piece of research, van der Wouden takes into account, not only semantic and syntactic considerations, but also to a large extent, pragmatic ones illustrating a wide array (...) of linguistic approaches. (shrink)

Modern logicians have sought to unlock the modal secrets of Aristotle's Syllogistic by assuming a version of essentialism and treating it as a primitive within the semantics. These attempts ultimately distort Aristotle's ontology. None of these approaches make full use of tests found throughout Aristotle's corpus and ancient Greek philosophy. I base a system on Aristotle's tests for things that can never combine (polarity) and things that can never separate (inseparability). The resulting system not only reproduces Aristotle's recorded results (...) for the apodictic syllogistic in the Prior Analytics but it also generates rather than assumes Aristotle's distinctions among 'necessary', 'essential' and 'accidental'. By developing a system around tests that are in Aristotle and basic to ancient Greek philosophy, the system is linked to a history of practices, providing a platform for future work on the origins of logic. (shrink)

We give the precise correspondence between polarized linear logic and polarized classical logic. The properties of focalization and reversion of linear proofs are at the heart of our analysis: we show that the tq-protocol of normalization for the classical systems and perfectly fits normalization of polarized proof-nets. Some more semantical considerations allow us to recover LC as a refinement of multiplicative.

This paper presents an analysis of negative polarity items (NPIs) in Hindi. It is noted that NPIs in this language are composed of a (weak) indefinite plus a particle bhii meaning ‘even’. It is argued that the compositional semantics of this combination explains their behavior as NPIs as well as their behavior as free choice (FC) items. I assume that weak Hindi indefinites like ek and koi are to be viewed as a predicate that I call one, a predicate (...) that is true of everything that exists. I further assume that bhii exhibits association with focus with the indefinite, and that this leads to contradictory implicatures in positive contexts. The behavior of these phrases in a variety of syntactic contexts is discussed, including constructions like correlatives. Finally, I provide a comparison with analyses of English any, and discuss the relevance of the analysis presented here for that of any. (shrink)

Semantic information is usually supposed to satisfy the veridicality thesis: p qualifies as semantic information only if p is true. However, what it means for semantic information to be true is often left implicit, with correspondentist interpretations representing the most popular, default option. The article develops an alternative approach, namely a correctness theory of truth (CTT) for semantic information. This is meant as a contribution not only to the philosophy of information but also to the philosophical (...) debate on the nature of truth. After the introduction, in Sect. 2, semantic information is shown to be translatable into propositional semantic information (i). In Sect. 3, i is polarised into a query (Q) and a result (R), qualified by a specific context, a level of abstraction and a purpose. This polarization is normalised in Sect. 4, where [Q + R] is transformed into a Boolean question and its relative yes/no answer [Q + A]. This completes the reduction of the truth of i to the correctness of A. In Sects. 5 and 6, it is argued that (1) A is the correct answer to Q if and only if (2) A correctly saturates Q by verifying and validating it (in the computer science’s sense of verification and validation ); that (2) is the case if and only if (3) [Q + A] generates an adequate model (m) of the relevant system (s) identified by Q; that (3) is the case if and only if (4) m is a proxy of s (in the computer science’s sense of proxy ) and (5) proximal access to m commutes with the distal access to s (in the category theory’s sense of commutation ); and that (5) is the case if and only if (6) reading/writing (accessing, in the computer science’s technical sense of the term) m enables one to read/write (access) s. Sect. 7 provides some further clarifications about CTT, in the light of semantic paradoxes. Section 8 draws a general conclusion about the nature of CTT as a theory for systems designers not just systems users. In the course of the article all technical expressions from computer science are explained. (shrink)

Alternatives in Semantics is the first volume to focus on alternatives as a key theme. It offers a survey of the use of alternatives in semantics and pragmatics, and an overview of current approaches and applications of alternative-based semantics, from both theoretical and experimental perspectives. The chapters represent different theoretical frameworks, which differ in the way they conceive of the source of alternatives, the status of alternatives, or the precise way in which they enter semantic composition. The contributions focus (...) on various empirical phenomena making reference to alternatives (negative polarity and free choice phenomena, implicatures, presupposition, focus and intervention effects), offering new insights and exploring connections between them. The chapters assembled in this volume demonstrate the vitality of alternative-based semantics and offer a clear perspective on the many challenging questions that arise from its increasing range of applications. (shrink)

This article offers a unified theory of the licensing of Negative and Positive Polarity Items, focusing on the acceptability conditions of PPIs of the some-type, and NPIs of the any-type. It argues that licensing has both a syntactic and a semantic component. On the syntactic side, the acceptability of PIs is checked in constituents; in fact, for any given PI, only some constituents, referred to as `domains', are eligible for the evaluation of that PI. The semantic dimension (...) of licensing consists in the sensitivity of PIs to the monotonicity properties of the syntactic environments they find themselves in. Two pieces of evidence support the semantic dimension of what I call the ‘environment-based’ approach defended here: PIs are subject to flip-flop and certain inferences affect their acceptability by modifying the monotonicity of their environment. A third property, called ‘entanglement’ and so far unnoticed, is described: the acceptability of PIs depends on the acceptability of other PIs in the same syntactic environment. The latter property is exploited to determine what semantic property some is sensitive to: it turns out that, contrary to the consensus among researchers, some is acceptable in the complement of the set of environments in which any is acceptable, and vice versa. (shrink)

The representation of Neg-Raising in the grammar is a matter of controversy. I provide evidence for representing Neg-Raising as a kind of presupposition associated with certain predicates by providing a detailed analysis of NPI-licensing in Neg-Raising contexts. Specific features of presupposition projection are used to explain the licensing of strict NPIs under Neg-Raising predicates. Discussion centers around the analysis of a licensing asymmetry noted in Horn (1971, Negative transportation: Unsafe at any speed? In CLS 7 (pp. 120–133)).Having provided this analysis, (...) I go on to discuss its implications for the theory of NPI-licensing more generally. In particular, I discuss how the present proposal reflects on von Fintel’s (1999, Journal of Semantics, 16, 97–148) proposal to use Strawson downward entailment in the statement of NPI-licensing principles. (shrink)

In this paper I provide a decompositional analysis of three kinds of plural indefinites in two related languages, European Spanish and Brazilian Portuguese. The three indefinites studied are bare plurals, the unos (Spanish)/uns (Portuguese) type, and the algunos (Spanish)/alguns (Portuguese) type. The paper concentrates on four properties: semantic plurality, positive polarity, partitivity, and event distribution. The logic underlying the analysis is that of compositionality, applied at the subword level: as items become bigger in form (with the addition of (...) morphemes), they also acquire more semantic properties. The paper proposes the “indefinite hierarchy", which establishes a set of components for languages to build their indefinites with, in a particular order. (shrink)

Sentences with slifting parentheticals The formal analysis of natural language, Mouton, The Hague, 1973) grammaticalize an intriguing interaction between truth-conditional meaning and speech act function. In such sentences, the assertion strength of the slifted clause is modulated by the parenthetical, which provides evidential support :480–496, 1952; Asher in J Semant 17:31–50, 2000; Rooryck in Glot Int 5:125–133, 2001; Jayez and Rossari in: Corblin, de Swart Handbook of French semantics, CSLI, Stanford, 2004; Davis et al. in Proc Semant Linguist Theory 17:71–88, (...) 2007; Simons in Lingua 117:1034–1056, 2007; Murray in Semant Pragmat 7:1–53, 2014; Maier and Bary in: Brochhagen et al. Proceedings of the 20th Amsterdam colloquium, 2015; AnderBois in Semant Pragmat 9:1–55, 2016; Hunter in Dialogue Discourse 7:1–35, 2016). Starting with the idea that assertability comes in degrees, this paper develops a probabilistic updatemodel that captures the role of parentheticality as a language tool for qualifying commitments. A crucial role here is played by the rule of Jeffrey conditionalization, which factors in the uncertainty of the parenthetical information itself. The model also derives certain effects of parenthetical modification not found in regular embedding constructions, including the fact that slifting parentheticals are limited to creating upward-entailing environments. (shrink)

In this paper we reconsider the issue of free choice and the role of the wh-morphology employed in it. We show that the property of being an interrogative wh-word alone is not sufficient for free choice, and that semantic and sometimes even morphological definiteness is a pre-requisite for some free choice items (FCIs) in certain languages, e.g. in Greek and Mandarin Chinese. We propose a theory that explains the polarity behaviour of FCIs cross-linguistically, and allows indefinite (Giannakidou 2001) (...) as well as definite-like FCIs. The difference is manifested as a lexical distinction in English between any (indefinite) and wh-ever (definite); in Greek it appears as a choice between a FCI nominal modifier (taking an NP argument), which illustrates the indefinite option, and a FC free relative illustrating the definite one. We provide a compositional analysis of Greek FCIs in both incarnations, and derive in a parallel manner the Chinese FCIs. Here the definite versus indefinite alternation is manifested in the presence or absence of dōu, which we take to express the maximality operator. It is thus shown that what we see in the morphology of FCIs in Greek is reflected in syntax in Chinese. Our analysis has important consequences for the class of so-called wh-indeterminates. In the context of current proposals, free choiceness is taken to come routinely from interrogative semantics, and wh-indeterminates are treated as question words which can freely become FCIs (Kratzer and Shimoyama 2002). Our results from Mandarin and Greek emphasize that wh-indeterminates do not form a uniform class in this respect, and that interrogative semantics alone cannot predict either sensitivity of free choice to definiteness, or the polarity behaviour of FCIs. (shrink)

We approach the semantics of prepositions from the perspective of conceptual spaces. Focusing on purely spatial locative and directional prepositions, we analyze both types of prepositions in terms of polar coordinates instead of Cartesian coordinates. This makes it possible to demonstrate that the property of convexity holds quite generally in the domain of prepositions of location and direction, supporting the important role that this property plays in conceptual spaces.

The concept of polarity is pervasive in natural language. It relates syntax, semantics and pragmatics narrowly, Semantics: an international handbook of natural language meaning, De Gruyter Mouton, Berlin, 2011; Israel in The grammar of polarity: pragmatics, sensitivity, and the logic of scales, Cambridge studies in linguistics, Cambridge University Press, Cambridge, 2014), it refers to items of many syntactic categories such as nouns, verbs and adverbs. Neutral polarity items appear in affirmative and negative sentences, negative polarity items (...) cannot appear in affirmative sentences, and positive polarity items cannot appear in negative sentences. A way of reasoning in Natural Language is through Natural Logic. This logic is based on the concept of polarity in order to make the meaning of a sentence weaker o stronger without changing its truth value. There exist many proposals to compute polarity in the Natural Logic context, the most widely known are the ones by: van Benthem, Sánchez-Valencia, Dowty, and van Eijck, 6th international Tbilisi symposium on logic, language, and computation, Batumi, Georgia, Springer, 2007). If Natural Logic is going to be used, as an inferential mechanism between text fragments, in Natural Language Processing applications such as text summarization, question answering, and information extraction, it is a priority to know what the existing relationship among the aforementioned algorithms is; for example, to implement the most general. We show in this paper the equivalence among the analyzed algorithms, filling a gap in Natural Logic research, particularly in computing polarity, and the soundness of their algorithms. (shrink)

Pesetsky’s (1987) ‘‘aggressively non-D-linked’’ wh-phrases (like who the hell; hereinafter, wh-the-hell phrases) exhibit a variety of syntactic and semantic peculiarities, including the fact that they cannot occur in situ and do not support nonecho readings when occurring in root multiple questions. While these are familiar from the literature (albeit less than fully understood), our focus will be on a previously unnoted property of wh-the-hell phrases: the fact that their distribution (in single wh-questions) matches that of polarity items (PIs). (...) We lay out the key data supporting this claim, embed the PI nature of wh-the-hell phrases in the theory of polarity developed in Giannakidou 1998, 1999, 2001, and establish the link between the lexical content of these phrases and their PI status by identifying wh-the-hell as a dependent PI. We subsequently exploit the PI status of wh-the-hell to explain the more familiar puzzles mentioned above, showing that these are not peculiarities specific to wh-the-hell but manifestations of the general properties of the class of PIs that wh-the-hell belongs to. The syntactic aspects of the polarity analysis of wh-the-hell are shown to have important consequences for the fundamental properties of wh-movement in English. (shrink)

I present an analysis of Free Choice Items (FCIs), based on Scandinavian, where FCIs are complex and distinct from polarity sensitive items. Scandinavian FCIs are argued to have two components. One is a universal quantifying into modal contexts. The other is an operator mapping a type (s,t) expression onto itself, adjoining to the closest type t or (s,t) expression. Thus invoking Intensional Functional Application, this operator requires the presence of a modal in the scope of the universal quantifier. Facts (...) concerning ‘essential connections’ and ‘existential import’ are accounted for by assuming that the FC determiner has the option of acting like a quantifier. (shrink)

The essays in this collection are the outgrowth of a workshop, held in June 1976, on formal approaches to the semantics and pragmatics of natural languages. They document in an astoundingly uniform way the develop ments in the formal analysis of natural languages since the late sixties. The avowed aim of the' workshop was in fact to assess the progress made in the application of formal methods to semantics, to confront different approaches to essentially the same problems on the one (...) hand, and, on the other, to show the way in relating semantic and pragmatic explanations of linguistic phenomena. Several of these papers can in fact be regarded as attempts to close the 'semiotic circle' by bringing together the syntactic, semantic and pragmatic properties of certain constructions in an explanatory framework thereby making it more than obvious that these three components of an integrated linguistic theory cannot be as neatly separated as one would have liked to believe. In other words, not only can we not elaborate a syntactic description of (a fragment of) a language and then proceed to the semantics (as Montague pointed out already forcefully in 1968), we cannot hope to achieve an adequate integrated syntax and semantics without paying heed to the pragmatic aspects of the constructions involved. The behavior of polarity items, 'quantifiers' like any, conditionals or even logical particles like and and or in non-indicative sentences is clear-cut evidence for the need to let each component of the grammar inform the other. (shrink)

The scalar approach to negative polarity item (NPI) licensing assumes that NPIs are allowable in contexts in which the introduction of the NPI leads to proposition strengthening (e.g., Kadmon & Landman 1993, Krifka 1995, Lahiri 1997, Chierchia 2006). A straightforward processing prediction from such a theory is that NPI’s facilitate inference verification from sets to subsets. Three experiments are reported that test this proposal. In each experiment, participants evaluated whether inferences from sets to subsets were valid. Crucially, we manipulated (...) whether the premises contained an NPI. In Experiment 1, participants completed a metalinguistic reasoning task, and Experiments 2 and 3 tested reading times using a self-paced reading task. Contrary to expectations, no facilitation was observed when the NPI was present in the premise compared to when it was absent. In fact, the NPI significantly slowed down reading times in the inference region. Our results therefore favor those scalar theories that predict that the NPI is costly to process (Chierchia 2006), or other, nonscalar theories (Giannakidou 1998, Ladusaw 1992, Postal 2005, Szabolcsi 2004) that likewise predict NPI processing cost but, unlike Chierchia (2006), expect the magnitude of the processing cost to vary with the actual pragmatics of the NPI. (shrink)

This paper examines distinctive discourse properties of preposed negative 'yes/no' questions (NPQs), such as 'Isn’t Jane coming too?'. Unlike with other 'yes/no' questions, using an NPQ '∼p?' invariably conveys a bias toward a particular answer, where the polarity of the bias is opposite of the polarity of the question: using the negative question '∼p?' invariably expresses that the speaker previously expected the positive answer p to be correct. A prominent approach—what I call the context-management approach, developed most extensively (...) by Romero and Han (2004)—attempts to capture speaker expectation biases by treating NPQs fundamentally as epistemic questions about the proper discourse status of a proposition. I raise challenges for existing context-managing accounts to provide more adequate formalizations of the posited context-managing content, its implementation in the compositional semantics and discourse dynamics, and its role in generating the observed biases. New data regarding discourse differences between NPQs and associated epistemic modal questions are introduced. I argue that we can capture the roles of NPQs in expressing speakers’ states of mind and managing the discourse common ground without positing special context-managing operators or treating NPQs as questions directly about the context. I suggest that we treat the operator introduced with preposed negation as having an ordinary semantics of epistemic necessity, though lexically associated with a general kind of endorsing use observed with modal expressions. The expressive and context-managing roles of NPQs are explained in terms of a general kind of discourse-oriented use of context-sensitive language. The distinctive expectation biases and discourse properties observed with NPQs are derived from the proposed semantics and a general principle of Discourse Relevance. (shrink)

We combine intuitionistic logic and classical logic into a new, first-order logic called polarized intuitionistic logic. This logic is based on a distinction between two dual polarities which we call red and green to distinguish them from other forms of polarization. The meaning of these polarities is defined model-theoretically by a Kripke-style semantics for the logic. Two proof systems are also formulated. The first system extends Gentzenʼs intuitionistic sequent calculus LJ. In addition, this system also bears essential similarities to Girardʼs (...) LC proof system for classical logic. The second proof system is based on a semantic tableau and extends Dragalinʼs multiple-conclusion version of intuitionistic sequent calculus. We show that soundness and completeness hold for these notions of semantics and proofs, from which it follows that cut is admissible in the proof systems and that the propositional fragment of the logic is decidable. (shrink)

Italian and English factives differ from each other in interesting and puzzling ways. English emotive factives license Negative Polarity Items, while their Italian counterparts don’t. Moreover, when factives of all kinds occur in the scope of negation in Italian an intervention effect emerges that interferes with NPI licensing way more robustly than in English. In this paper, I explore the idea that this contrast between Italian and English may be due to a difference in the Complementizer -system of the (...) two languages that parallels a difference that has been noted in the literature between the singular and the plural definite determiner the with respect to NPI licensing. Understanding how factives differ across languages with respect to polarity phenomena is not only interesting in its own right, but also because it sheds further light on how logical contradictions may affect grammaticality judgments. (shrink)

The main focus of this article is the occurrence of some polarity items (PIs) in the complements of emotive factive verbs and only. This fact has been taken as a challenge to the semantic approach to PIs (Linebarger 1980), because only and factive verbs are not downward entailing (DE). A modification of the classical DE account is proposed by introducing the notion of nonveridicality (Zwarts 1995, Giannakidou 1998, 1999, 2001) as the one crucial for PI sanctioning. To motivate (...) this move, it is first shown that two solutions in the direction of weakening classical monotonicity do not work: Strawson DE (von Fintel 1999) and weak DE (Hoeksema 1986). Weakening DE systematically either overgenerates or undergenerates, in either case failing to characterize the correct set of licensers. Nonveridicality is introduced as a conservative extension of DE and is shown to account for PIs also in contexts that are not DE (i.e. questions, modal verbs, imperatives, directive propositional attitudes). This theory, augmented with the premise that certain PIs (i.e. the liberal class represented by any) are subject to a weaker polarity dependency identified not as LICENSING but as RESCUING by nonveridicality, explains the occurrence of this particular class with only and emotive factive verbs. Crosslinguistic comparisons illustrate that the occurrence of PIs with only and emotive factives is not a general phenomenon, and further support the dual nature of polarity dependency and the semantic characterization of the elements that license or rescue PIs. (shrink)

Negative Concord (NC) constructions such as the news anchor didn’t warn nobody about the floods (meaning ‘the news anchor warned nobody’), in which two syntactic negations contribute a single semantic one, are stigmatized in English, while their Negative Polarity Item (NPI) variants, such as the news anchor didn’t warn anybody about the floods, are prescriptively correct. Equating acceptability with grammaticality, this pattern has led linguists to treat NC as ungrammatical in “Standard” or standardized English (SE). However, it is (...) possible that SE grammars do generate NC sentences, and their low incidence and acceptability is instead due to social factors. To explore this question, and the relationship between NC and NPI constructions, we compared the acceptability of overtly negative noun phrases (e.g. nobody), NPIs (e.g. anybody), and bare plurals (e.g. people), in negative contexts and in conditionals. Negative items were followed by a consequence which supported their single negative meaning, while conditional items were followed by a consequence compatible with the NPI and the bare plural but not the negative noun phrase. Acceptability ratings of the critical NC sentences were reliably lower than constructions with NPIs and bare plurals, but the consequences for all three of these sentence types were rated highly. This reflects an asymmetry in participants’ acceptance of NC and their readiness to interpret it in context. A follow-up study with only conditionals revealed that speakers can also find NPIs infelicitous in conditional contexts with consequences that are compatible with a negative interpretation of the NPI, and that negative arguments are felicitous in these same contexts. Taken together, the results support the hypothesis that speakers who do not accept NC have grammars that generate both NC and NPI constructions, and further, that these speakers have two underlying structures for any-NPIs in English. (shrink)

The argument here comes from consideration of a certain sort of linguistic expression called negative polarity items (NPIs). These are expressions such as “any,” “at all” and “ever.” NPIs are of particular interest for semantics because they can only be used in contexts with a certain rather abstract semantic feature. However, the precise characterization of the feature is itself a matter of some controversy. For those interested in the semantics of natural language it is worthwhile to figure out (...) precisely what this feature is. Once we have an account of it, we can use the account to infer facts about the meanings of various expressions that interact with NPIs. (shrink)

I show that speaker bias in _polarity focus questions_ (PFQs) is context sensitive, while speaker bias in _high negation questions_ (HNQs) is context insensitive. This leads me to develop separate accounts of speaker bias in each of these kinds of polar questions. I argue that PFQ bias derives from the fact that they are frequently used in conversational contexts in which an answer to the question has already been asserted by an interlocutor, thus expressing doubt about the prior assertion. This (...) derivation explains their context sensitivity, and the fact that similar bias arises from polar questions that lack polarity focus. I also provide novel evidence that the prejacents of HNQs lack negation, and thus only have an outer negation reading (see, e.g., Ladd in Papers from the seventeenth regional meeting of the Chicago Linguistic Society, vol. 17, pp. 164–171, 1981 ; Romero and Han in Linguistics and Philosophy 27(5):609–658, 2004 ; Krifka in Contrastiveness in information structure, alternatives and scalar implicatures, pp. 359–398, 2017 ; AnderBois in Questions in discourse, pp. 118–171, 2019 ; Frana and Rawlins in Semantics and Pragmatics 12(16):1–48, 2019 ; Jeong in Journal of Semantics 38(1):49–94, 2020 ). Based on a treatment of HNQs as denoting unbalanced partitions (Romero and Han in Linguistics and Philosophy 27(5):609–658, 2004 ), and competition with their positive polar question alternatives, I propose a novel derivation of speaker bias in HNQs as a conversational implicature. Roughly, if the speaker is ignorant, then a positive polar question will be more useful because it is more informative, so the use of an HNQ conveys that the speaker is not ignorant. The denotation of the HNQ then makes clear which way the speaker is biased. The result separates high negation from verum focus, and I argue that it is more parsimonious and has better empirical coverage than prior accounts. (shrink)

This paper reviews a series of experimental studies that address what we call ‘interface judgement’, which is the complex judgment involving integration from multiple levels of grammatical representation such as the syntax-semantics and prosody-semantics interface. We first discuss the results from the ERP literature connected to NPI licensing in different languages, paying particular attention to the N400 and the P600 as neural correlates of this specific phenomenon and focusing on the study by Xiang et al. (2016). The results of this (...) study show evidence that there are two distinct NPI licensing mechanisms, i.e., licensing and rescuing, in line with Giannakidou (1998, 2006). Then we discuss an acceptability judgement task on Greek NPIs which supports the negativity as a scale hypothesis (Zwarts 1995, 1996, Giannakidou 1998). For the semantics-prosody interface judgment, we discuss two types of findings on two different phenomena and languages: (i) the study by Giannakidou & Yoon (2016) on scalar and non-scalar NPIs in Greek and Korean, which serves as the foundation for Chatzikontantinou (2016)’s study of production data showing distinct prosodic properties in emphatic (scalar) and non-emphatic (non-scalar) Greek NPIs; (ii) a (production and perception) study by Etxeberria & Irurtzun (2015) on the prosodic disambiguation of the scalar/non-scalar readings of sentences containing the focus particle ‘ere’ in Basque. The main conclusion of the paper is that experimental methods of the kind discussed in the paper are useful in establishing physical, quantitative correlates of interface judgement. (shrink)