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  • Ken Akiba (2009). A New Theory of Quantifiers and Term Connectives. Journal of Logic, Language and Information 18 (3).
    This paper sets forth a new theory of quantifiers and term connectives, called shadow theory , which should help simplify various semantic theories of natural language by greatly reducing the need of Montagovian proper names, type-shifting, and λ-conversion. According to shadow theory, conjunctive, disjunctive, and negative noun phrases such as John and Mary , John or Mary , and not both John and Mary , as well as determiner phrases such as every man , some woman , and the boys (...)
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  • Natasha Alechina (2000). Functional Dependencies Between Variables. Studia Logica 66 (2).
    We consider a predicate logic Lfd where not all assignments of values to individual variables are possible. Some variables are functionally dependent on other variables. This makes sense if the models of logic are assumed to correspond to databases or states. We show that Lfd is undecidable but has a complete and sound sequent calculus formalisation.
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  • Aldo Antonelli, Free Quantification and Logical Invariance.
    Henry Leonard and Karel Lambert first introduced so-called presupposition-free (or just simply: free) logics in the 1950’s in order to provide a logical framework allowing for non-denoting singular terms (be they descriptions or constants) such as “the largest prime” or “Pegasus” (see Leonard [1956] and Lambert [1960]). Of course, ever since Russell’s paradigmatic treatment of definite descriptions (Russell [1905]), philosophers have had a way to deal with such terms. A sentence such as “the..
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  • Kent Bach (2000). Quantification, Qualification and Context a Reply to Stanley and Szabó. Mind and Language 15 (2&3):262–283.
    We hardly ever mean exactly what we say. I don’t mean that we generally speak figuratively or that we’re generally insincere. Rather, I mean that we generally speak loosely, omitting words that could have made what we meant more explicit and letting our audience fill in the gaps. Language works far more efficiently when we do that. Literalism can have its virtues, as when we’re drawing up a contract, programming a computer, or writing a philosophy paper, but we generally opt (...)
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  • Kent Bach (1982). Semantic Nonspecificity and Mixed Quantifiers. Linguistics and Philosophy 4 (4).
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  • S. J. Barker (1997). E-Type Pronouns, DRT, Dynamic Semantics and the Quantifier/Variable-Binding Model. Linguistics and Philosophy 20 (2).
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  • John A. Barnden & Kankanahalli Srinivas (1996). Quantification Without Variables in Connectionism. Minds and Machines 6 (2).
    Connectionist attention to variables has been too restricted in two ways. First, it has not exploited certain ways of doing without variables in the symbolic arena. One variable-avoidance method, that of logical combinators, is particularly well established there. Secondly, the attention has been largely restricted to variables in long-term rules embodied in connection weight patterns. However, short-lived bodies of information, such as sentence interpretations or inference products, may involve quantification. Therefore short-lived activation patterns may need to achieve the effect of (...)
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  • JC Beall, Ross T. Brady, A. P. Hazen, Graham Priest & Greg Restall (2006). Relevant Restricted Quantification. Journal of Philosophical Logic 35 (6).
    The paper reviews a number of approaches for handling restricted quantification in relevant logic, and proposes a novel one. This proceeds by introducing a novel kind of enthymematic conditional.
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  • Nuel D. Belnap Jr (1970). Conditional Assertion and Restricted Quantification. Noûs 4 (1):1-12.
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  • Gilad Ben-Avi & Yoad Winter (2003). Monotonicity and Collective Quantification. Journal of Logic, Language and Information 12 (2).
    This article studies the monotonicity behavior of plural determinersthat quantify over collections. Following previous work, we describe thecollective interpretation of determiners such as all, some andmost using generalized quantifiers of a higher type that areobtained systematically by applying a type shifting operator to thestandard meanings of determiners in Generalized Quantifier Theory. Twoprocesses of counting and existential quantification thatappear with plural quantifiers are unified into a single determinerfitting operator, which, unlike previous proposals, both capturesexistential quantification with plural determiners and respects theirmonotonicity (...)
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  • Johan Benthem (1989). Polyadic Quantifiers. Linguistics and Philosophy 12 (4).
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  • Claudia Bianchi (2006). 'Nobody Loves Me': Quantification and Context. Philosophical Studies 130 (2).
    In my paper, I present two competing perspectives on the foundational problem (as opposed to the descriptive problem) of quantifier domain restriction: the objective perspective on context (OPC) and the intentional perspective on context (IPC). According to OPC, the relevant domain for a quantified sentence is determined by objective facts of the context of utterance. In contrast, according to IPC, we must consider certain features of the speaker’s intention in order to determine the proposition expressed. My goal is to offer (...)
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  • Robert Binkley (1970). Quantifying, Quotation, and a Paradox. Noûs 4 (3):271-277.
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  • Andrea Bonomi (1997). Aspect, Quantification and When-Clauses in Italian. Linguistics and Philosophy 20 (5).
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  • George Boolos (1984). To Be is to Be a Value of a Variable (or to Be Some Values of Some Variables). Journal of Philosophy 81 (8):430-449.
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  • E. P. Brandon (1982). Quantifiers and the Pursuit of Truth. Educational Philosophy and Theory 14 (1):51–58.
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  • Adrian Brasoveanu, Structured Anaphora to Quantifier Domains: A Unified Account of Quantificational and Modal Subordination.
    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 (...)
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  • Adrian Brasoveanu (2008). Donkey Pluralities: Plural Information States Versus Non-Atomic Individuals. Linguistics and Philosophy 31 (2).
    The paper argues that two distinct and independent notions of plurality are involved in natural language anaphora and quantification: plural reference (the usual non-atomic individuals) and plural discourse reference, i.e. reference to a quantificational dependency between sets of objects (e.g. atomic / non-atomic individuals) that is established and subsequently elaborated upon in discourse. Following van den Berg (1996), plural discourse reference is modeled as plural information states (i.e. as sets of variable assignments) in a new dynamic system couched in classical (...)
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  • Joseph L. Camp Jr (1975). Truth and Substitution Quantifiers. Noûs 9 (2):165-185.
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  • Ian F. Carlstrom (1975). Truth and Entailment for a Vague Quantifier. Synthese 30 (3-4).
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  • Rudolf Carnap (1946). Modalities and Quantification. Journal of Symbolic Logic 11 (2):33-64.
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  • Robin Clark & Murray Grossman (2007). Number Sense and Quantifier Interpretation. Topoi 26 (1).
    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.
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  • Nino B. Cocchiarella (1992). Conceptual Realism Versus Quine on Classes and Higher-Order Logic. Synthese 90 (3).
    The problematic features of Quine's set theories NF and ML are a result of his replacing the higher-order predicate logic of type theory by a first-order logic of membership, and can be resolved by returning to a second-order logic of predication with nominalized predicates as abstract singular terms. We adopt a modified Fregean position called conceptual realism in which the concepts (unsaturated cognitive structures) that predicates stand for are distinguished from the extensions (or intensions) that their nominalizations denote as singular (...)
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  • Peter Cole (1985). Quantifier Scope and the ECP. Linguistics and Philosophy 8 (2).
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  • John Collins, Names, Descriptions and Quantifiers.
    (1) Singular terms Singular term : a word or phrase that refers to an individual object; its semantic value is an object.
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  • Sean Crawford (2008). Quantifiers and Propositional Attitudes: Quine Revisited. Synthese 160 (1).
    Quine introduced a famous distinction between the ‘notional’ sense and the ‘relational’ sense of certain attitude verbs. The distinction is both intuitive and sound but is often conflated with another distinction Quine draws between ‘dyadic’ and ‘triadic’ (or higher degree) attitudes. I argue that this conflation is largely responsible for the mistaken view that Quine’s account of attitudes is undermined by the problem of the ‘exportation’ of singular terms within attitude contexts. Quine’s system is also supposed to suffer from the (...)
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  • Mary Dalrymple, John Lamping, Fernando Pereira & Vijay Saraswat (1997). Quantifiers, Anaphora, and Intensionality. Journal of Logic, Language and Information 6 (3).
    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 (...)
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  • Martin Davies (1989). 'Two Examiners Marked Six Scripts.' Interpretations of Numerically Quantified Sentences. Linguistics and Philosophy 12 (3).
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  • Paul Dekker (2008). A Multi-Dimensional Treatment of Quantification in Extraordinary English. Linguistics and Philosophy 31 (1).
    In this paper I revive two important formal approaches to the interpretation of natural language, that of Montague and that of Karttunen and Peters. Armed with insights from dynamic semantics (Heim, Krifka) the two turn out to stand up against age-old criticisms in an orthodox fashion. The plan is mainly methodological, as I only want to illustrate the technical feasibility of the revived proposals. Even so, there are illuminating and welcome empirical consequences on the subject of scope islands (as discussed (...)
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  • Nicholas Denyer (1999). Names, Verbs and Quantification Again. Philosophy 74 (3):439-440.
    There are enormous differences between quantifying name-variables only, quantifying verb-variables only, and quantifying both. These differences are found only in the logic of polyadic predication; and this presumably is why Richard Gaskin thinks that they distinguish names from transitive verbs only, and not from verbs generally. But that thought is mistaken: these differences also distinguish names from intransitive verbs. They thus vindicate the common idea that on the difference between names and verbs we may base grandiose metaphysical distinctions, and undermine (...)
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  • Jaap Does (1993). Sums and Quantifiers. Linguistics and Philosophy 16 (5).
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  • Stephen Donaho (2002). Standard Quantification Theory in the Analysis of English. Journal of Philosophical Logic 31 (6).
    Standard first-order logic plus quantifiers of all finite orders (SFOL) faces four well-known difficulties when used to characterize the behavior of certain English quantifier phrases. All four difficulties seem to stem from the typed structure of SFOL models. The typed structure of SFOL models is in turn a product of an asymmetry between the meaning of names and the meaning of predicates, the element-set asymmetry. In this paper we examine a class of models in which this asymmetry of meaning is (...)
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  • J. Michael Dunn (1970). Conditional Assertion and Restricted Quantification: Abstracts of Comments. Noûs 4 (1):13.
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  • Donka F. Farkas & Adrian Brasoveanu, Scope and the Grammar of Choice.
    and Data The essence of scope in natural language semantics can be characterized as follows: an expression e1 takes scope over an expression e2 iff the interpretation of the former affects the interpretation of the latter. Consider, for example, the sentence in (1) below, which is typical of the cases discussed in this paper in that it involves an indefinite and a universal (or, more generally, a non-existential) quantifier. (1) Everyx student in my class read ay paper about scope. How (...)
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  • Tim Fernando, Conservative Generalized Quantifiers and Presupposition.
    Conservativity in generalized quantifiers is linked to presupposition filtering, under a propositions-as-types analysis extended with dependent quantifiers. That analysis is underpinned by modeltheoretically interpretable proofs which inhabit propositions they prove, thereby providing objects for quantification and hooks for anaphora.
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  • Kit Fine, Relatively Unrestricted Quantification.
    There are four broad grounds upon which the intelligibility of quantification over absolutely everything has been questioned—one based upon the existence of semantic indeterminacy, another on the relativity of ontology to a conceptual scheme, a third upon the necessity of sortal restriction, and the last upon the possibility of indefinite extendibility. The argument from semantic indeterminacy derives from general philosophical considerations concerning our understanding of language. For the Skolem–Lowenheim Theorem appears to show that an understanding of quanti- fication over absolutely (...)
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  • Janet Dean Fodor & Ivan A. Sag (1982). Referential and Quantificational Indefinites. Linguistics and Philosophy 5 (3).
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  • Enrico Franconi (1993). A Treatment of Plurals and Plural Quantifications Based on a Theory of Collections. Minds and Machines 3 (4).
    Collective entities and collective relations play an important role in natural language. In order to capture the full meaning of sentences like The Beatles sing Yesterday, a knowledge representation language should be able to express and reason about plural entities — like the Beatles — and their relationships — like sing — with any possible reading (cumulative, distributive or collective).In this paper a way of including collections and collective relations within a concept language, chosen as the formalism for representing the (...)
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  • Kazuhiko Fukushima (1991). Phrase Structure Grammar, Montague Semantics, and Floating Quantifiers in Japanese. Linguistics and Philosophy 14 (6).
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  • Anastasia Giannakidou, Domain Restriction and the Arguments of Quantificational Determiners.
    Classical generalized quantifier (GQ) theory posits that quantificational determiners (Q-dets) combine with a nominal argument of type et, a first order predicate, to form a GQ. In a recent paper, Matthewson (2001) challenges this position by arguing that the domain of a Q-det is not of type et, but e, an entity. In this paper, I defend the classical GQ view, and argue that the data that motivated Matthewson’s revision actually suggest that the domain set can, and indeed in certain (...)
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  • Anastasia Giannakidou, Giannakidou and Rathert, Eds. Quantification, Definiteness, and Nominalization.
    The papers in this volume are updated versions of talks that were presented at the workshop QP structure, Nominalizations, and the role of DP that we organized at Saarland University, Germany, in December 2005. Although the connection between QP structure and definiteness, on the one hand, and nominalizations and definiteness on the other, were long observed in the literature, there has never been an attempt to bring the three together, and our aim at the workshop was to do exactly this: (...)
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  • David Gil (1982). Quantifier Scope, Linguistic Variation, and Natural Language Semantics. Linguistics and Philosophy 5 (4).
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  • Michael Glanzberg, Quantifiers.
    Quantified terms are terms of generality. They are also provide some of our prime examples of the phenomenon of scope. The distinction between singular and general terms, as well as the ways that general terms enter into scope relations, are certainly fundamental to our understanding of language. Yet when we turn to natural language, we encounter a huge and apparently messy collection of general terms; not just every and some, but most, few, between five and ten, and many others. Natural-language (...)
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  • Michael Glanzberg (2008). Quantification and Contributing Objects to Thoughts. Philosophical Perspectives 22 (1):207-231.
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  • Michael Glanzberg (2006). Context and Unrestricted Quantification. In Michael Glanzberg (ed.). Oxford University Press.
    Quantification is haunted by the specter of paradoxes. Since Russell, it has been a persistent idea that the paradoxes show what might have appeared to be absolutely unrestricted quantification to be somehow restricted. In the contemporary literature, this theme is taken up by Dummett (1973, 1993) and Parsons (1974a,b). Parsons, in particular, argues that both the Liar and Russell’s paradoxes are to be resolved by construing apparently absolutely unrestricted quantifiers as appropriately restricted.
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  • Theodore Hailperin (1957). A Theory of Restricted Quantification I. Journal of Symbolic Logic 22 (1):19-35.
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  • Theodore Hailperin (1957). A Theory of Restricted Quantification II. Journal of Symbolic Logic 22 (2):113-129.
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  • Michael Hand (1993). A Defense of Branching Quantification. Synthese 95 (3).
    Adding branching quantification to a first-order language increases the expressive power of the language,without adding to its ontology. The present paper is a defense of this claim against Quine (1970) and Patton (1991).
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  • Katherine Hawley, Neo-Fregeanism and Quantifier Variance.
    Sider argues that, of maximalism and quantifier variance, the latter promises to let us make better sense of neo-Fregeanism. I argue that neo-Fregeans should, and seemingly do, reject quantifier variance. If they must choose between these two options, they should choose maximalism.
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  • Jim Higginbotham (1994). Mass and Count Quantifiers. Linguistics and Philosophy 17 (5).
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