We give a complete proof that all 3 quantifier sentences in the primitive notation of set theory (Œ,=), are decided in ZFC, and in fact in a weak fragment of ZF without the power set axiom. We obtain information concerning witnesses of 2 quantifier formulas with one free variable. There is a 5 quantifier sentence that is not decided in ZFC (see [Fr02]).

We present a set-theoretic model of the mental representation of classically quantified sentences (All P are Q, Some P are Q, Some P are not Q, and No P are Q). We take inclusion, exclusion, and their negations to be primitive concepts. We show that although these sentences are known to have a diagrammatic expres- sion (in the form of the Gergonne circles) that constitutes a semantic representation, these concepts can also be expressed syntactically in the form (...) of algebraic formulas. We hypothesized that the quantified sen- tences have an abstract underlying representation common to the formulas and their associated sets of dia- grams (models). We derived 9 predictions (3 semantic, 2 pragmatic, and 4 mixed) regarding people’s as- sessment of how well each of the 5 diagrams expresses the meaning of each of the quantified sentences. We report the results from 3 experiments using Gergonne’s (1817) circles or an adaptation of Leibniz (1903/ 1988) lines as external representations and show them to support the predictions. (shrink)

Some theories assume that sentences like (i) with a presupposition trigger in the scope of a quantifier carry an existential presupposition, as in (ii); others assume that they carry a universal presupposition, as in (iii). No student knows that he is lucky. Existential presupposition: At least one student is lucky.Universal presupposition: Every student is lucky. This work is an experimental investigation of this issue in French. Native speakers were recruited to evaluate the robustness of the inference from (i) to (...) (iii). The main result is that presuppositions triggered from the scope of the quantifier aucun‘no’ are in fact universal. But the present results also suggest that the presuppositions triggered from the scope of other quantifiers depend on the quantifier. This calls for important changes in the main theories of presupposition projection. (shrink)

We present a set-theoretic model of the mental representation of classically quantified sentences (All P are Q, Some P are Q, Some P are not Q, and No P are Q). We take inclusion, exclusion, and their negations to be primitive concepts. It is shown that, although these sentences are known to have a diagrammatic expression (in the form of the Gergonne circles) which constitute a semantic representation, these concepts can also be expressed syntactically in the form (...) of algebraic formulas. It is hypothesized that the quantified sentences have an abstract underlying representation common to the formulas and their associated sets of diagrams (models). Nine predictions are derived (three semantic, two pragmatic, and four mixed) regarding people's assessment of how well each of the five diagrams expresses the meaning of each of the quantified sentences. The results from three experiments, using Gergonne's circles or an adaptation of Leibniz lines as external representations, are reported and shown to support the predictions. (shrink)

Natural language sentences that talk about two or more sets of entities can be assigned various readings. The ones in which the sets are independent of one another are particularly challenging from the formal point of view. In this paper we will call them ‘Independent Set (IS) readings’. Cumulative and collective readings are paradigmatic examples of IS readings. Most approaches aiming at representing the meaning of IS readings implement some kind of maximality conditions on the witness sets involved. Two (...) kinds of maximization have been proposed in the literature: ‘Local’ and ‘Global’ maximization. In this paper, we present an online questionnaire whose results appear to support Local maximization. The latter seems to capture the proper interplay between the semantics and the pragmatics of multi-quantifier sentences, provided that witness sets are selected on pragmatic grounds. (shrink)

The paper proposes the first unified account of deictic/sentence-external and sentence-internal readings of singular different . The empirical motivation for such an account is provided by a cross-linguistic survey and an analysis of the differences in distribution and interpretation between singular different , plural different and same (singular or plural) in English. The main proposal is that distributive quantification temporarily makes available two discourse referents within its nuclear scope, the values of which are required by sentence-internal uses of singular different (...) to be distinct, much as its deictic uses require the values of two discourse referents to be distinct. Thus, we take sentence-internal readings to be a form of ‘association with distributivity’ that is similar to association with focus. The contrast between singular different , plural different and same is explained in terms of several kinds of quantificational distributors that license their internal readings. The analysis is executed in a stack-based dynamic system couched in type logic, so we get compositionality in the usual Montagovian way. Quantificational subordination and dependent indefinites in various languages provide additional motivation for the account. Investigating the connections between items with sentence-internal readings and the quantificational licensors of these readings opens up a larger project of formally investigating (i) the typology of quantificational distributors and distributivity-dependent items and (ii) the fine-grained contexts of evaluation needed to capture this typological variation. (shrink)

the Central Division of the APA in Chicago, April 19-21 2007. The paper proposes an account of conditional donkey sentences, such as ‘if a farmer buys a donkey, he usually vaccinates it’, which accommodates the fact that the adverb of quantification seems to affect the interpretation of pronouns that are not within its syntactic scope. The analysis defended takes donkey pronouns to go proxy for partitive noun phrases with varying quantificational force. The variation in the interpretation of donkey pronouns, (...) it is argued, is determined by the linguistic environment in which the pronouns occur. A longer version of this paper can be found in the works in progress section below. (shrink)

1. Ramsey Sentences and the Function of Theoretical Concepts. In his famous paper “Theories,” Frank Ramsey introduced a technique of examining a scientific theory by means of certain propositions, dubbed later “Ramsey Sentences.” They are the results of what is often called Ramsey elimination. This prima facie elimination is often presented as a method of dispensing with theoretical concepts in scientific theorizing. The idea is this: Assume that we are given a finitely axiomatized scientific theorywhere O1, O2, … (...) are the primitive observation terms of and H1, H2, … its primitive theoretical terms. For simplicity, it will be assumed that is a first-order theory. Since it is finitely axiomatizable, we may think of it as having the form of a single complex proposition, i.e., the conjunction of all the axioms. What can then be done is to generalize existentially with respect to. The result is a sentence of the formIn, the theoretical terms H1, H2, … do not occur any longer. They have been replaced by the variables X1, X2, … bound to initial existential quantifiers. In this sense at least, Ramsey sentences do effect on elimination. Unlike, is not a first-order sentence but a second-order one. (shrink)

In this paper we present a logical system able to compute the semantics of both declarative and interrogative sentences. Our proposed analysis takes place at both the sentential and at the discourse level. We use syntactic inference on the sentential level for declarative sentences, while the discourse level comes into play for our treatment of questions. Our formalization uses a type logic sensitive to both the syntactic and semantic properties of natural language. We will show how an account (...) of the linguistic data follows naturally from the logical relations inherent in the type logic. (shrink)

The traditional Square of Opposition consists of four sentence types. Two are universal and two particular; two are affirmative and two negative. Examples, where ‘S’ and ‘P’ designate the subject and the predicate, are: ‘every S is P’, ‘no S is P’, ‘some S is P’ and ‘some S is not P’. Taking the usual sentences of the square of opposition, quantifying over their predicates exhibits non-standard sentence forms. These sentences may be combined into non-standard Squares of Opposition (...) , and they reveal a new relationship not found in the usual Square. Medieval logicians termed ‘disparatae’ pairs of sentences like ‘every S is some P’ and ‘some S is every P’, which are neither subaltern nor contrary, neither contradictory nor subcontrary. Walter Redmond has designed a special language L to express the logical form of these sentences in a precise way. I will use this language to show how Squares of Opposition, standard and non-standard, form a complex network of relations which bring to .. (shrink)

Quantified expressions in natural language generally are taken to act like quantifiers in logic, which either range over entities that need to satisfy or not satisfy the predicate in order for the sentence to be true or otherwise are substitutional quantifiers. I will argue that there is a philosophically rather important class of quantified expressions in English that act quite differently, a class that includes something, nothing, and several things. In addition to expressing quantification, such expressions act like (...) nominalizations, introducing a new domain of objects that would not have been present in the semantic structure of the sentence otherwise. The entities those expressions introduce are of just the same sort as those that certain ordinary nominalizations refer to (such as John's wisdom or John's belief that S), namely they are tropes or entities related to tropes. Analysing certain quantifiers as nominalizing quantifiers will shed a new light on philosophical issues such as the status of properties and the nature of propositional attitudes. (shrink)

This volume on the semantic complexity of natural language explores the question why some sentences are more difficult than others. While doing so, it lays the groundwork for extending semantic theory with computational and cognitive aspects by combining linguistics and logic with computations and cognition. -/- Quantifier expressions occur whenever we describe the world and communicate about it. Generalized quantifier theory is therefore one of the basic tools of linguistics today, studying the possible meanings and the inferential power of (...) quantifier expressions by logical means. The classic version was developed in the 1980s, at the interface of linguistics, mathematics and philosophy. Before this volume, advances in "classic" generalized quantifier theory mainly focused on logical questions and their applications to linguistics, this volume adds a computational component, the third pillar of language use and logical activity. This book is essential reading for researchers in linguistics, philosophy, cognitive science, logic, AI, and computer science. (shrink)

I develop a formal logic in which quantified arguments occur in argument positions of predicates. This logic also incorporates negative predication, anaphora and converse relation terms, namely, additional syntactic features of natural language. In these and additional respects, it represents the logic of natural language more adequately than does any version of Frege’s Predicate Calculus. I first introduce the system’s main ideas and familiarize it by means of translations of natural language sentences. I then develop a formal system (...) built on these principles, the Quantified Argument Calculus or Quarc. I provide a truth-value assignment semantics and a proof system for the Quarc. I next demonstrate the system’s power by a variety of proofs; I prove its soundness; and I comment on its completeness. I then extend the system to modal logic, again providing a proof system and a truth-value assignment semantics. I proceed to show how the Quarc versions of the Barcan formulas, of their converses and of necessary existence come out straightforwardly invalid, which I argue is an advantage of the modal Quarc over modal Predicate Logic as a system intended to capture the logic of natural language. (shrink)

Henkin quantifiers have been introduced in Henkin (1961). Walkoe (1970) studied basic model-theoretical properties of an extension $L_{*}^{1}$ (H) of ordinary first-order languages in which every sentence is a first-order sentence prefixed with a Henkin quantifier. In this paper we consider a generalization of Walkoe's languages: we close $L_{*}^{1}$ (H) with respect to Boolean operations, and obtain the language L¹(H). At the next level, we consider an extension $L_{*}^{2}$ (H) of L¹(H) in which every sentence is an L¹(H)-sentence prefixed with (...) a Henkin quantifier. We repeat this construction to infinity. Using the (un)definability of truth - in - N for these languages, we show that this hierarchy does not collapse. In addition, we compare some of the present results to the ones obtained by Kripke (1975), McGee (1991), and Hintikka (1996). (shrink)

In the dissertation we study the complexity of generalized quantifiers in natural language. Our perspective is interdisciplinary: we combine philosophical insights with theoretical computer science, experimental cognitive science and linguistic theories. -/- In Chapter 1 we argue for identifying a part of meaning, the so-called referential meaning (model-checking), with algorithms. Moreover, we discuss the influence of computational complexity theory on cognitive tasks. We give some arguments to treat as cognitively tractable only those problems which can be computed in polynomial time. (...) Additionally, we suggest that plausible semantic theories of the everyday fragment of natural language can be formulated in the existential fragment of second-order logic. -/- In Chapter 2 we give an overview of the basic notions of generalized quantifier theory, computability theory, and descriptive complexity theory. -/- In Chapter 3 we prove that PTIME quantifiers are closed under iteration, cumulation and resumption. Next, we discuss the NP-completeness of branching quantifiers. Finally, we show that some Ramsey quantifiers define NP-complete classes of finite models while others stay in PTIME. We also give a sufficient condition for a Ramsey quantifier to be computable in polynomial time. -/- In Chapter 4 we investigate the computational complexity of polyadic lifts expressing various readings of reciprocal sentences with quantified antecedents. We show a dichotomy between these readings: the strong reciprocal reading can create NP-complete constructions, while the weak and the intermediate reciprocal readings do not. Additionally, we argue that this difference should be acknowledged in the Strong Meaning hypothesis. -/- In Chapter 5 we study the definability and complexity of the type-shifting approach to collective quantification in natural language. We show that under reasonable complexity assumptions it is not general enough to cover the semantics of all collective quantifiers in natural language. The type-shifting approach cannot lead outside second-order logic and arguably some collective quantifiers are not expressible in second-order logic. As a result, we argue that algebraic (many-sorted) formalisms dealing with collectivity are more plausible than the type-shifting approach. Moreover, we suggest that some collective quantifiers might not be realized in everyday language due to their high computational complexity. Additionally, we introduce the so-called second-order generalized quantifiers to the study of collective semantics. -/- In Chapter 6 we study the statement known as Hintikka's thesis: that the semantics of sentences like ``Most boys and most girls hate each other'' is not expressible by linear formulae and one needs to use branching quantification. We discuss possible readings of such sentences and come to the conclusion that they are expressible by linear formulae, as opposed to what Hintikka states. Next, we propose empirical evidence confirming our theoretical predictions that these sentences are sometimes interpreted by people as having the conjunctional reading. -/- In Chapter 7 we discuss a computational semantics for monadic quantifiers in natural language. We recall that it can be expressed in terms of finite-state and push-down automata. Then we present and criticize the neurological research building on this model. The discussion leads to a new experimental set-up which provides empirical evidence confirming the complexity predictions of the computational model. We show that the differences in reaction time needed for comprehension of sentences with monadic quantifiers are consistent with the complexity differences predicted by the model. -/- In Chapter 8 we discuss some general open questions and possible directions for future research, e.g., using different measures of complexity, involving game-theory and so on. -/- In general, our research explores, from different perspectives, the advantages of identifying meaning with algorithms and applying computational complexity analysis to semantic issues. It shows the fruitfulness of such an abstract computational approach for linguistics and cognitive science. (shrink)

Modal sentences of the form "every F might be G" and "some F must be G" have a threefold ambiguity. in addition to the familiar readings "de dicto" and "de re", there is a third reading on which they are examples of the "plural de re": they attribute a modal property to the F's plurally in a way that cannot in general be reduced to an attribution of modal properties to the individual F's. The plural "de re" readings of (...) modal sentences cannot be captured within standard quantified modal logic. I consider various strategies for extending standard quantified modal logic so as to provide analyses of the readings in question. I argue that the ambiguity in question is associated with the scope of the general term 'F'; and that plural quantifiers can be introduced for purposes of representing the scope of a general term. Moreover, plural quantifiers provide the only fully adequate solution that keeps within the framework of quantified modal logic. (shrink)

I here argue that Ted Sider's indeterminacy argument against vagueness in quantifiers fails. Sider claims that vagueness entails precisifications, but holds that precisifications of quantifiers cannot be coherently described: they will either deliver the wrong logical form to quantified sentences, or involve a presupposition that contradicts the claim that the quantifier is vague. Assuming (as does Sider) that the “connectedness” of objects can be precisely defined, I present a counter-example to Sider's contention, consisting of a partial, implicit definition (...) of the existential quantifier that in effect sets a given degree of connectedness among the putative parts of an object as a condition upon there being something (in the sense in question) with those parts. I then argue that such an implicit definition, taken together with an “auxiliary logic” (e.g., introduction and elimination rules), proves to function as a precisification in just the same way as paradigmatic precisifications of, e.g., “red”. I also argue that with a quantifier that is stipulated as maximally tolerant as to what mereological sums there are, precisifications can be given in the form of truth-conditions of quantified sentences, rather than by implicit definition. (shrink)

As Quine observed, the following sentence has a reading which, if true, would be of special interest to the authorities: Ralph believes that someone is a spy. This is the reading where the quantifier is naturally understood as taking wide scope relative to the attitude verb and as binding a variable within the scope of the attitude verb. This essay is interested in addressing the question what the semantic analysis of this kind of reading should look like from a Fregean (...) perspective—a perspective according to which attitude states are generally relations to structured Fregean thoughts composed of senses. The Fregean view faces a challenge of compositionality here. This essay describes the challenge and offers a response on the Fregean's behalf. (shrink)

In discussing propositional quantifiers we have considered two kinds of variables: variables occupying the argument places of connectives, and variables occupying the argument places of predicates.We began with languages which contained the first kind of variable, i.e., variables taking sentences as substituends. Our first point was that there appear to be no sentences in English that serve as adequate readings of formulas containing propositional quantifiers. Then we showed how a certain natural and illuminating extension of English by prosentences (...) did provide perspicuous readings. The point of introducing prosentences was to provide a way of making clear the grammar of propositional variables: propositional variables have a prosentential character — not a pronominal character. Given this information we were able to show, on the assumption that the grammar of propositional variables in philosopher's English should be determined by their grammar in formal languages (unless a separate account of their grammar is provided), that propositional variables can be used in a grammatically and philosophically acceptable way in philosophers' English. According to our criteria of well-formedness Carnap's semantic definition of truth does not lack an ‘essential’ predicate - despite arguments to the contrary. It also followed from our account of the prosentential character of bound propositional variables that in explaining propositional quantification, sentences should not be construed as names.One matter we have not discussed is whether such quantification should be called ‘propositional’, ‘sentential’, or something else. As our variables do not range over (they are not terms) either propositions, or sentences, each name is inappropriate, given the usual picture of quantification. But we think the relevant question in this context is, are we obtaining generality with respect to propositions, sentences, or something else?Because people have argued that all bound variables must have a pronominal character, we presented and discussed in the third section languages in which the variables take propositional terms as substituends. In our case we included names of propositions, that-clauses, and names of sentences in the set of propositional terms. We made a few comparisons with the languages discussed in the second section. We showed among other things how a truth predicate could be used to obtain generality. In contrast, the languages of the second section, using propositional variables, obtain generality without the use of a truth predicate. (shrink)

The paper develops a set of quantified temporal alethic boulesic doxastic systems. Every system in this set consists of five parts: a ‘quantified’ part, a temporal part, a modal (alethic) part, a boulesic part and a doxastic part. There are no systems in the literature that combine all of these branches of logic. Hence, all systems in this paper are new. Every system is defined both semantically and proof-theoretically. The semantic apparatus consists of a kind of$$T \times W$$T×Wmodels, (...) and the proof-theoretical apparatus of semantic tableaux. The ‘quantified part’ of the systems includes relational predicates and the identity symbol. The quantifiers are, in effect, a kind of possibilist quantifiers that vary over every object in the domain. The tableaux rules are classical. The alethic part contains two types of modal operators for absolute and historical necessity and possibility. According to ‘boulesic logic’ (the logic of the will), ‘willing’ (‘consenting’, ‘rejecting’, ‘indifference’ and ‘non-indifference’) is a kind of modal operator. Doxastic logic is the logic of beliefs; it treats ‘believing’ (and ‘conceiving’) as a kind of modal operator. I will explore some possible relationships between these different parts, and investigate some principles that include more than one type of logical expression. I will show that every tableau system in the paper is sound and complete with respect to its semantics. Finally, I consider an example of a valid argument and an example of an invalid sentence. I show how one can use semantic tableaux to establish validity and invalidity and read off countermodels. These examples illustrate the philosophical usefulness of the systems that are introduced in this paper. (shrink)

We investigate uncertain reasoning with quantified sentences of the predicate calculus treated as the limiting case of maximum entropy inference applied to finite domains.

That the result of flipping quantifiers and negating what comes after, applied to branching-quantifier sentences, is not equivalent to the negation of the original has been known for as long as such sentences have been studied. It is here pointed out that this syntactic operation fails in the strongest possible sense to correspond to any operation on classes of models.

We study the computational complexity of polyadic quantifiers in natural language. This type of quantification is widely used in formal semantics to model the meaning of multi-quantifier sentences. First, we show that the standard constructions that turn simple determiners into complex quantifiers, namely Boolean operations, iteration, cumulation, and resumption, are tractable. Then, we provide an insight into branching operation yielding intractable natural language multi-quantifier expressions. Next, we focus on a linguistic case study. We use computational complexity results to investigate (...) semantic distinctions between quantified reciprocal sentences. We show a computational dichotomy<br>between different readings of reciprocity. Finally, we go more into philosophical speculation on meaning, ambiguity and computational complexity. In particular, we investigate a possibility to<br>revise the Strong Meaning Hypothesis with complexity aspects to better account for meaning shifts in the domain of multi-quantifier sentences. The paper not only contributes to the field of the formal<br>semantics but also illustrates how the tools of computational complexity theory might be successfully used in linguistics and philosophy with an eye towards cognitive science. (shrink)

A person of average height would assert a truth by the conditional ‘if I were seven feet tall, I would be taller than I am,’ in which an indicative clause ‘I am’ is embedded in a subjunctive conditional. By contrast, no one would assert a truth by ‘if I were seven feet tall, I would be taller than I would be’ or ‘if I am seven feet tall, I am taller than I am’. These examples exemplify the fact that whether (...) a sentence's evaluation remains at the actual world in the scope of a modal or conditional depends on the combination of mood in the embedded and matrix clauses rather than, as is commonly thought, just on the presence of an operator ‘actually’. This essay argues that this phenomenon provides evidence that mood admits of bound and free readings along the lines of tenses and pronouns. It therefore favors the hypothesis that natural language contains variables and quantifiers for possible worlds in the object language. This, in turn, requires that the truth of a semantic value of a sentence (or whatever structure is embedded in a modal) be relativized to a sequence of worlds rather than to an individual world, and thus be distinguished from a proposition in the traditional sense. The essay also compares the framework defended with an alternative account of similar phenomena by Kai Wehmeier. (shrink)

Information‐theoretic complexity metrics, such as Surprisal (Hale, 2001; Levy, 2008) and Entropy Reduction (Hale, 2003), are linking hypotheses that bridge theorized expectations about sentences and observed processing difficulty in comprehension. These expectations can be viewed as syntactic derivations constrained by a grammar. However, this expectation‐based view is not limited to syntactic information alone. The present study combines structural and non‐structural information in unified models of word‐by‐word sentence processing difficulty. Using probabilistic minimalist grammars (Stabler, 1997), we extend expectation‐based models to (...) include frequency information about noun phrase animacy. Entropy reductions derived from these grammars faithfully reflect the asymmetry between subject and object relatives (Staub, 2010; Staub, Dillon, & Clifton, 2017), as well as the effect of animacy on the measured difficulty profile (Lowder & Gordon, 2012; Traxler, Morris, & Seely, 2002). Visualizing probability distributions on the remaining alternatives at particular parser states allows us to explore new, linguistically plausible interpretations for the observed processing asymmetries, including the way that expectations about the relativized argument influence the processing of particular types of relative clauses (Wagers & Pendleton, 2016). (shrink)

Hintikka’s semantic approach to meaning, a development of Wittgenstein’s view of meaning as use, is the general theme of this chapter. We will focus on the analysis of quantified sentences and on the scope of the principle of compositionality and compare Hintikka’s take on these issues with that of Frege. The aim of this paper is to show that Hintikka’s analysis of quantified expressions as choice functions, in spite of its obvious dissimilarities with respect to the higher-order (...) approach, is actually very close to the Fregean stance on compositionality and context dependence. In particular, we will defend that the Fregean approach to quantifiers is unavoidably linked to the idea that quantified expressions are context-dependent, and therefore should not be conceived under the traditional inside-out model for analysis. (shrink)

The relationship between Lexical-Functional Grammar (LFG) functional structures (f-structures) for sentences and their semanticinterpretations can be formalized in linear logic in a way thatcorrectly explains the observed interactions between quantifier scopeambiguity, bound anaphora and intensionality.Our linear-logic formalization of the compositional properties ofquantifying expressions in natural language obviates the need forspecial mechanisms, such as Cooper storage, in representing thescoping possibilities of quantifying expressions. Instead, thesemantic contribution of a quantifier is recorded as a linear-logicformula whose use in a proof will establish (...) the scope of thequantifier. Different proofs can lead to different scopes. In eachcomplete proof, the properties of linear logic ensure thatquantifiers are properly scoped. (shrink)

In this paper I discuss two objections raised against von Fintel’s (1994) and Stanley and Szabó’s (2000a) hidden variable approach to quantifier domain restriction (QDR). One of them concerns utterances of sentences involving quantifiers for which no contextual domain restriction is needed, and the other concerns multiple quantified contexts. I look at various ways in which the approaches could be amended to avoid these problems, and I argue that they fail. I conclude that we need a more flexible (...) account of QDR, one that allows for the hidden variables in the LF responsible for QDR to vary in number. Recanati’s (2002; 2004) approach to QDR, which makes use of the apparatus of “variadic functions”, is flexible enough to account successfully for the two phenomena discussed. I end with a few comments on what I take to be the most promising way to construe variadic functions. (shrink)

The sentence Irving was closer to me than he was to most of the others contains a quantifier, most of the other, in the scope a comparative. The first part of this paper explains the challenges presented by such cases to existing approaches to the semantics of the comparative. The second part presents a new analysis of comparatives based on intervals rather than points on a scale. This innovation is analogized to the move from moments to intervals in tense semantics. (...) The remainder of the paper is concerned with an interval-based semantics of degree in relation to issues other than the comparative proper. The paper begins with a discussion of the role negative polarity has played in studies on the semantics of comparatives. (shrink)

Stephen Barker (The Philosophical Quarterly, 47 (1997), pp. 195–211) has presented a new argument for a pure material implication analysis of indicative conditionals. His argument relies crucially on the assumption that general indicatives such as ‘Every girl, if she gets a chance, bungee‐jumps’ are correctly analysed as having the formal structure (for all x)(if x gets a chance, x bungee‐jumps). This paper argues that an approach first proposed by David Lewis must be pursued: the ‘if’‐clause in these sentences restricts (...) the quantifier. Only the Lewis‐style analysis can deal with sentences involving non‐universal quantifiers such as ‘Most letters are answered if they are shorter than 5 pages’. I show that Barker's reasons for rejecting the restrictor analysis are not cogent and that the restrictor analysis connects widely with recent work in natural language semantics. (shrink)

This dissertation investigates the ways in which natural language restricts the domains of quantifiers. Adverbs of quantification are analyzed as quantifying over situations. The domain of quantifiers is pragmatically constrained: apparent processes of "semantic partition" are treated as pragmatic epiphenomena. The introductory Chapter 1 sketches some of the background of work on natural language quantification and begins the analysis of adverbial quantification over situations. Chapter 2 develops the central picture of "semantic partition" as a side-effect of pragmatic processes of anaphora (...) resolution. I argue that the apparent effects of topic/focus articulation and presuppositional information on the interpretation of quantifiers are not the result of a direct and local mechanism of sentence grammar. Instead, I develop an analysis where the link is established via the anaphoric dependence of quantifier domains on the discourse context. Chapter 3 discusses the analysis of conditional clauses as quantifier restrictors, concentrating on the question whether conditional clauses restrict quantifiers directly or indirectly. A treatment is explored which has if-clauses constrain the value of the hidden domain variable of the restricted quantifier. Chapter 4, on unless-clauses, and Chapter 5, on only if- and even if-clauses, present some issues in the compositional analysis of complex conditional clauses. These chapters significantly expand the data coverage of the theory of A-quantification. Building on previous work of mine on exceptives, I analyze unless-clauses as exceptive operators on A-quantifiers. The analysis of only if-clauses, treated as conditional clauses that combine if with the focus adverb only, unearthes some interesting new properties. Chapter 6, finally, examines the phenomenon of donkey-anaphora in the light of the results of the previous chapters. I show that a solution to the proportion problem may become possible once we combine the situation-semantic approach to adverbial quantification with the pragmatic theory developed in Chapter 2 and further elaborated in the analysis of donkey anaphora in complex conditionals. (shrink)

In this paper, I have proposed a compositional semantic analysis of exception NPs from which three core properties of exception constructions could be derived. I have shown that this analysis overcomes various empirical and conceptual shortcomings of prior proposals of the semantics of exception sentences. The analysis was first formulated for simple exception NPs, where the EP-complement was considered a set-denoting term and the EP-associate was a monadic quantifier. It was then generalized in two steps: first, in order to (...) account for quantified EP-complements, and second, in order to account for polyadic quantifiers as the EP-associates. An additional assumption that was made in several places was that EPs may operate at the level of implications. The consequences of this assumption, though, still have to be investigated. (shrink)

We design new languages, by and large, in order to bypass complexities and limitations within the languages we already have. But when we are concerned with language itself we should guard against projecting the simple and powerful syntax and semantics we have concocted back into the sentences we encounter. For some of the features of English, French, or Ancient Greek we routinely abstract away from in the process of formalization might be linguistic universals – the very features that set (...) human languages apart from all the other conceivable ones. How similar natural languages really are to formal ones is an empirical question for linguistics. (shrink)

The paper proposes an account of the contrast (noticed in Karttunen 1976) between the interpretations of the following two discourses: Harvey courts a girl at every convention. {She is very pretty. vs. She always comes to the banquet with him.}. The initial sentence is ambiguous between two quantifier scopings, but the first discourse as a whole allows only for the wide-scope indefinite reading, while the second allows for both. This cross-sentential interaction between quantifier scope and anaphora is captured by means (...) of a new dynamic system couched in classical type logic, which extends Compositional DRT (Muskens 1996) with plural information states (modeled, following van den Berg 1996, as sets of variable assignments). Given the underlying type logic, compositionality at sub-clausal level follows automatically and standard techniques from Montague semantics become available. The paper also shows that modal subordination (A wolf might come in. It would eat Harvey first) can be analyzed in a parallel way, i.e. the system captures the anaphoric and quantificational parallels between the individual and modal domains argued for in Stone (1999) (among others). In the process, we see that modal / individual-level quantifiers enter anaphoric connections as a matter of course, usually functioning simultaneously as both indefinites and pronouns. (shrink)

This investigation draws from research on negative polarity item (NPI) illusions in order to explore a new and interesting instance of misalignment observed for grammatical sentences containing two negative markers. Previous research has shown that unlicensed NPIs can be perceived as acceptable when occurring soon after a structurally inaccessible negation (e.g. ever in *The bills that no senators voted for have ever become law). Here we examine the opposite configuration: grammatical sentences created by substituting the NPI ever with (...) the negative adverb never (e.g. The bills that no senators voted for have never become law). The processing and acceptability of these sentences was studied using three tasks: a speeded acceptability judgment (experiment 1), a self-paced reading task (experiment 2), and an offline acceptability rating (experiment 3). The results are consistent across measures in showing that the integration of the adverb never is disrupted by the linearly preceding but structurally inaccessible negative quantifier no in the relative clause. In our view, this pattern of results is in line with Parker and Phillips’ (2016) proposal that NPI illusions arise when the context containing the inaccessible negation has not been fully encoded by the time the NPI ever is encountered, making the embedded negative quantifier transparently available as a licensor. In a similar vein, the disruption effects observed for grammatical sentences containing two negative elements could arise if the negative quantifier is still being integrated when never is encountered, forcing the parser to deal with two negative elements simultaneously. This interpretation suggests that the same incomplete encodings that could be ameliorating the online perception of unlicensed NPIs could also be responsible for deteriorating the perception of the sentences under investigation here. This would represent an illusion of ungrammaticality. Furthermore, these results provide evidence against the speculation that NPI illusions are the consequence of misrepresenting ever as its near neighbor never, given that continuations with never are judged as unacceptable in spite of their grammaticality. Together, these findings inform the landscape of hypotheses on NPI illusions and offer valuable insights on the complexity of multiple negation and the relation between processing difficulty and acceptability. (shrink)

* This work has been evolving for a while now. Some parts trace back to the few pages on the context-dependency of quantifiers in my dissertation. Reading Recanati’s paper on domains of discourse made me rethink some of my earlier conclusions without in the end actually changing them much. Other parts formed the material for several discussions in my seminar on context-dependency at MIT in the fall of 1995, which included several sessions exploring the issues raised in an early version (...) of Kratzer. Connecting the choice function approach to indefinites with a general analysis of contextual domain restriction was an idea that I considered then without however working out any details. Conversations with Lisa Matthewson and studying her paper inspired me to tackle the problem again. Connections to questions about the context-dependency of conditional sentences also tickled my fancy, since I have been working on conditionals for a while now. Having the opportunity to present this material at the Vilem Mathesius Series provided the impetus to flesh out some of my vague thoughts. Major influences come from the work done in recent years at MIT by Lisa Matthewson, Philippe Schlenker, Julie Legate, and Uli Sauerland. I thank Irene Heim, Lisa Matthewson, Orin Percus, Philippe Schlenker, and Jason Stanley for illuminating discussions about this material. At this point, I see this talk as a report on the state of the art, exploring an intriguing possible connection, but I do not claim substantial intellectual property rights. Mistakes are certainly mine, achievements are probably not. (shrink)

✤ It is the characterization of those forms of reasoning that lead invariably from true sentences to true sentences, independently of the subject matter.

We consider connections between number sense—the ability to judge number—and the interpretation of natural language quantifiers. In particular, we present empirical evidence concerning the neuroanatomical underpinnings of number sense and quantifier interpretation. We show, further, that impairment of number sense in patients can result in the impairment of the ability to interpret sentences containing quantifiers. This result demonstrates that number sense supports some aspects of the language faculty.

This volume is an outgrowth of the second Workshop on Logic, Language and Computation held at Stanford in the spring of 1993. The workshop brought together researchers interested in natural language to discuss the current state of the art at the borderline of logic, linguistics and computer science. The papers in this collection fall into three central research areas of the nineties, namely quantifiers, deduction, and context. Each contribution reflects an ever-growing interest in a more dynamic approach to meaning, which (...) focuses on inference patterns and the interpretation of sentences in the context of a larger discourse. The papers apply either current logical machinery - such as linear logic, generalised quantifier theory, dynamic logic - or formal analyses of the notion of context in discourse to classical linguistic issues, with original and thought-provoking results deserving of a wide audience. (shrink)

Conditional sentences with quantifying expressions are systematically ambigous. In one reading, the if -clause restricts the domain of the overt quantifier; in the other, the if -clause restricts the domain of a covert quantifier, which defaults to epistemic necessity. Although the ambiguity follows directly from the Lewis- Kratzer line on if, it is not generally acknowledged, which has led to pseudoproblems and spurious arguments.