This paper discusses two ways of negating DP quantifier phrases. In one way, NEG modifies the quantifier D directly with the structure [[NEG D] NP]. In the other way, NEG modifies the whole DP with the structure [NEG DP]. I give evidence based on negative polarity items that negated universal quantifier phrases like not every student involve outer negation.

The paper argues that natural language quantification, as expressed by determiner phrases, is not polysemous. The foil for this claim is Hofweber, who contends that natural language quantification is polysemous between a domain reading and an inferential reading. The thesis is intended to support a more general division between externalist and internalist positions in semantics. The paper, to the contrary, argues that there is no linguistic evidence for polysemous quantification, and Hofweber’s proposal proves to be non-compositional. Further, an approach at (...) least consistent with internalism is available independent of an inferential reading, for natural language quantification can be read as ontologically neutral, which removes the rationale for the polysemy hypothesis. The paper remains neutral on so-called heavyweight vs. lightweight construals of quantification, which are not claims about natural language semantics. (shrink)

This paper introduces a compositional semantics of locativeprepositional phrases which is based on a vector space ontology.Model-theoretic properties of prepositions like monotonicity andconservativity are defined in this system in a straightforward way.These notions are shown to describe central inferences with spatialexpressions and to account for the grammaticality of prepositionmodification. Model-theoretic constraints on the set of possibleprepositions in natural language are specified, similar to the semanticuniversals of Generalized Quantifier Theory.

The semantic automata framework, developed originally in the 1980s, provides computational interpretations of generalized quantifiers. While recent experimental results have associated structural features of these automata with neuroanatomical demands in processing sentences with quantifiers, the theoretical framework has remained largely unexplored. In this paper, after presenting some classic results on semantic automata in a modern style, we present the first application of semantic automata to polyadic quantification, exhibiting automata for iterated quantifiers. We also discuss the role of semantic automata in (...) linguistic theory and offer new empirical predictions for sentence processing with embedded quantifiers. (shrink)

Peters and Westerståhl (Quantifiers in Language and Logic, 2006), and Westerståhl (New Perspectives on the Square of Opposition, 2011) draw a crucial distinction between the “classical” Aristotelian squares of opposition and the “modern” Duality squares of opposition. The classical square involves four opposition relations, whereas the modern one only involves three of them: the two horizontal connections are fundamentally distinct in the Aristotelian case (contrariety, CR vs. subcontrariety, SCR) but express the same Duality relation of internal negation (SNEG). Furthermore, the (...) vertical relations in the classical square are unidirectional, whereas in the modern square they are bidirectional. The present paper argues that these differences become even bigger when two more operators are added, namely the U ( ${{\equiv} {\rm A}\,{\vee} \,{\rm E} }$ , all or no) and Y ( ${\equiv{\rm I} \,{\wedge} \,{\rm O}}$ , some but not all) of Blanché (Structures Intellectuelles, 1969). In the resulting Aristotelian hexagon the two extra nodes are perfectly integrated, yielding two interlocking triangles of CR and SCR. In the duality hexagon by contrast, they do not enter into any relation with the original square, but constitute a independent pair of their own, since they are their own SNEGs. Hence, they not only stand in a relation of external NEG, but also in one of duality. This reflexive nature of the SNEG will be shown to result in defective monotonicity configurations for the pair, namely the absence of right-monotonicity (on the predicate argument). In the second half of the paper, we present an overview of those hexagonal structures which are both Aristotelian and Duality configurations, and those which are only Aristotelian. (shrink)

Although it was traditionally thought that self-reference is a crucial ingredient of semantic paradoxes, Yablo (1993, 2004) showed that this was not so by displaying an infinite series of sentences none of which is self-referential but which, taken together, are paradoxical. Yablo's paradox consists of a countable series of linearly ordered sentences s(0), s(1), s(2),... , where each s(i) says: For each k > i, s(k) is false (or equivalently: For no k > i is s(k) true). We generalize Yablo's (...) results along two dimensions. First, we study the behavior of generalized Yablo-series in which each sentence s(i) has the form: For Q k > i, s(k) is true, where Q is a generalized quantifier (e.g., no, every, infinitely many, etc). We show that under broad conditions all the sentences in the series must have the same truth value, and we derive a characterization of those values of Q for which the series is paradoxical. Second, we show that in the Strong Kleene trivalent logic Yablo's results are a special case of a more general fact: under certain conditions, any semantic phenomenon that involves self-reference can be emulated without self-reference. Various translation procedures that eliminate self-reference from a non-quantificational language are defined and characterized. An Appendix sketches an extension to quantificational languages, as well as a new argument that Yablo's paradox and the translations we offer do not involve self-reference. (shrink)

Heim 1983 suggested that the analysis of presupposition projection requires that the classical notion of meanings as truth conditions be replaced with a dynamic notion of meanings as Context Change Potentials. But as several researchers (including Heim herself) later noted, the dynamic framework is insufficiently predictive: although it allows one to state that, say, the dynamic effect of F and G is to first update a Context Set C with F and then with G (i.e., C[F and G] = C[F][G]), (...) it fails to explain why there couldn’t be a ‘deviant’ conjunction and* which performed these operations in the opposite order (i.e., C[F and* G] = C[G][F]). We provide a formal introduction to a competing framework, the Transparency theory, which addresses this problem. Unlike dynamic semantics, our analysis is fully classical, i.e., bivalent and static. And it derives the projective behavior of connectives from their bivalent meaning and their syntax. We concentrate on the formal properties of a simple version of the theory, and we prove that (i) full equivalence with Heim’s results is guaranteed in the propositional case (Theorem 1), and that (ii) the equivalence can be extended to the quantificational case (for any generalized quantifiers), but only when certain conditions are met (Theorem 2). (shrink)

In this paper, I will argue for a new account of presuppositions which is based on double indexing as well as minimal representational contexts providing antecedent material for anaphoric presuppositions, rather than notions of context defined in terms of the interlocutors’ pragmatic presuppositions or the information accumulated from the preceding discourse. This account applies in particular to new phenomena concerning the presupposition of quantifier domains. But it is also intended to be an account of presuppositions in general. The account differs (...) from the Satisfaction Theory and the Binding Theory of presuppositions in that it can be viewed as a conservative extension of traditional static semantics and in that it does not involve the notion of pragmatic presupposition. (shrink)

The standard analysis of quantification says that determiner quantifiers (such as every) take an NP predicate and create a generalized quantifier. The goal of this paper is to subject these beliefs to crosslinguistic scrutiny. I begin by showing that in St'á'imcets (Lillooet Salish), quantifiers always require sisters of argumental type, and the creation of a generalized quantifier from an NP predicate always proceeds in two steps rather than one. I then explicitly adopt the strong null hypothesis that the denotations of (...) quantifiers should be crosslinguistically uniform. Since the Salish data cannot be captured by the usual analysis of English, I pursue the idea that English is reducible to the Salish pattern. Reanalysis of many English constructions is required. I argue that the reanalysis has advantages over the standard analysis for partitives, as well as for non-partitive all- and most-phrases, which I analyze as containing bare plurals of argumental type. Even where the new analysis faces some challenges (for example, with every), the attempt still leads to fruitful results. It forces us to view familiar constructions in a new light, and to redefine, I believe correctly, which quantificational constructions are ‘basic’ and which stand in need of further explanation. (shrink)

Many philosophers believe in things, propositions, which are the things that we believe, assert etc., and which are the contents of sentences. The act-type theory of propositions is an attempt to say what propositions are, to explain how we stand in relations to them, and to explain why they are true or false. The core idea of the act-type theory is that propositions are types of acts of predication. The theory is developed in various ways to offer explanations of the (...) important properties of propositions. I present the core idea of the theory, and some developments of it. I discuss the relationship between the theory and the content–force distinction. I also present an important type of objection that has been raised to the explanations offered by the act-type theory. (shrink)

Limited distribution phenomena related to negation and negative polarity are usually thought of in terms of affectivity where affective is understood as negative or downward entailing. In this paper I propose an analysis of affective contexts as nonveridical and treat negative polarity as a manifestation of the more general phenomenon of sensitivity to (non)veridicality (which is, I argue, what affective dependencies boil down to). Empirical support for this analysis will be provided by a detailed examination of affective dependencies in Greek, (...) but the distribution of any will also be shown to follow from (non)veridicality. (shrink)

We define and prove a formal semantics divided into two complementary interacting components: the strictly linguistic semantics, we call linguistic agent, and the strictly logical and referential semantics, we call rational agent. This Linguistic \ Rational Agents’ Semantics applies to Deep Dependency trees or more generally, to discourses, i.e. sequences of DD-trees, and interprets them by functional structures we call Meaning Representation Structures, similar to the DRT, but interpreted very differently. LRA semantics incrementally interprets the discourses by minimal finite models, (...) called proto-models, in a monotonic logic of the LA and checks the proto-models with respect to the classical models of the RA. The proto-model is considered as the linguistic sense of the discourse. We define in full detail the LA which, as we believe, must be universal. On the other hand, we don’t propose a particular RA. We only define the scheme of interaction between the two agents and the stimuli of the RA used by the LA. After all, every discourse has in LRA semantics the single meaning and the single sense for every Rational Agent used to interact with the Linguistic Agent. (shrink)

This article reveals a tension between a fairly standard response to "liar sentences," of which -/- (L) Sentence (L) -/- is not true is an instance, and some features of our natural language determiners (e.g., 'every,' 'some,' 'no,' etc.) that have been established by formal linguists. The fairly standard response to liar sentences, which has been voiced by a number of philosophers who work directly on the Liar paradox (e.g., Parsons [1974], Kripke [1975], Burge [1979], Goldstein [1985, 2009], Gaifman [1992, (...) 2000]), Glanzberg [2004], Azzouni [2006], and others), but can also be heard from philosophers who do not work directly on that paradox, is that liar sentences do not express propositions. Call this the "No Proposition View" (hereafter NPV). Evidently, the belief that liar sentences do not express propositions is a deeply held intuition. As the previously mentioned tension will reveal, there is reason to worry about whether this deeply held intuition can be sustained. (shrink)

I show that the contemporary dominant analysis of natural language quantifiers that are one-place determiners by means of binary generalized quantifiers has failed to explain why they are, according to it, conservative. I then present an alternative, Geachean analysis, according to which common nouns in the grammatical subject position are plural logical subject-terms, and show how it does explain that fact and other features of natural language quantification.

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)