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Generalized Quantifiers in Linguistics and Logic

In J. F. A. K. Van Benthem, Johan van Benthem & Alice G. B. Ter Meulen (eds.), Handbook of Logic and Language. Elsevier. pp. 837--893 (1997)

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  1. Number determiners, numbers, and arithmetic.Thomas Hofweber - 2005 - Philosophical Review 114 (2):179-225.
    In his groundbreaking Grundlagen, Frege (1884) pointed out that number words like ‘four’ occur in ordinary language in two quite different ways and that this gives rise to a philosophical puzzle. On the one hand ‘four’ occurs as an adjective, which is to say that it occurs grammatically in sentences in a position that is commonly occupied by adjectives. Frege’s example was (1) Jupiter has four moons, where the occurrence of ‘four’ seems to be just like that of ‘green’ in (...)
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  • Proportions in time: interactions of quantification and aspect. [REVIEW]Peter Hallman - 2009 - Natural Language Semantics 17 (1):29-61.
    Proportional quantification and progressive aspect interact in English in revealing ways. This paper investigates these interactions and draws conclusions about the semantics of the progressive and telicity. In the scope of the progressive, the proportion named by a proportionality quantifier (e.g. most in The software was detecting most errors) must hold in every subevent of the event so described, indicating that a predicate in the scope of the progressive is interpreted as an internally homogeneous activity. Such an activity interpretation is (...)
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  • On the grammar and processing of proportional quantifiers: most versus more than half.Martin Hackl - 2009 - Natural Language Semantics 17 (1):63-98.
    Abstract Proportional quantifiers have played a central role in the development of formal semantics because they set a benchmark for the expressive power needed to describe quantification in natural language (Barwise and Cooper Linguist Philos 4:159–219, 1981). The proportional quantifier most, in particular, supplied the initial motivation for adopting Generalized Quantifier Theory (GQT) because its meaning is definable as a relation between sets of individuals, which are taken to be semantic primitives in GQT. This paper proposes an alternative analysis of (...)
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  • The processing of polar quantifiers, and numerosity perception.Isabelle Deschamps, Galit Agmon, Yonatan Loewenstein & Yosef Grodzinsky - 2015 - Cognition 143 (C):115-128.
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  • Negation and negative concord in romance.Ivan A. Sag & Henriëtte De Swart - 2002 - Linguistics and Philosophy 25 (4):373-417.
    This paper addresses the two interpretations that a combination ofnegative indefinites can get in concord languages like French:a concord reading, which amounts to a single negation, and a doublenegation reading. We develop an analysis within a polyadic framework,where a sequence of negative indefinites can be interpreted as aniteration of quantifiers or via resumption. The first option leadsto a scopal relation, interpreted as double negation. The secondoption leads to the construction of a polyadic negative quantifiercorresponding to the concord reading. Given that (...)
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  • Generalized Quantifiers and Number Sense.Robin Clark - 2011 - Philosophy Compass 6 (9):611-621.
    Generalized quantifiers are functions from pairs of properties to truth-values; these functions can be used to interpret natural language quantifiers. The space of such functions is vast and a great deal of research has sought to find natural constraints on the functions that interpret determiners and create quantifiers. These constraints have demonstrated that quantifiers rest on number and number sense. In the first part of the paper, we turn to developing this argument. In the remainder, we report on work in (...)
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  • Scope dominance with upward monotone quantifiers.Alon Altman, Ya'Acov Peterzil & Yoad Winter - 2005 - Journal of Logic, Language and Information 14 (4):445-455.
    We give a complete characterization of the class of upward monotone generalized quantifiers Q1 and Q2 over countable domains that satisfy the scheme Q1 x Q2 y φ → Q2 y Q1 x φ. This generalizes the characterization of such quantifiers over finite domains, according to which the scheme holds iff Q1 is ∃ or Q2 is ∀ (excluding trivial cases). Our result shows that in infinite domains, there are more general types of quantifiers that support these entailments.
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  • Background notions in lattice theory and generalized quantifiers.Anna Szabolcsi - 1997 - In Ways of Scope Taking. Kluwer Academic Publishers. pp. 1--27.
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  • Ways of Scope Taking.Anna Szabolcsi (ed.) - 1997 - Kluwer Academic Publishers.
    Ways of Scope Taking is concerned with syntactic, semantic and computational aspects of scope. Its starting point is the well-known but often neglected fact that different types of quantifiers interact differently with each other and other operators. The theoretical examination of significant bodies of data, both old and novel, leads to two central claims. (1) Scope is a by-product of a set of distinct Logical Form processes; each quantifier participates in those that suit its particular features. (2) Scope interaction is (...)
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  • Symmetric and contrapositional quantifiers.R. Zuber - 2006 - Journal of Logic, Language and Information 16 (1):1-13.
    The article studies two related issues. First, it introduces the notion of the contraposition of quantifiers which is a “dual” notion of symmetry and has similar relations to co-intersectivity as symmetry has to intersectivity. Second, it shows how symmetry and contraposition can be generalised to higher order type quantifiers, while preserving their relations with other notions from generalized quantifiers theory.
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  • Positive polarity - negative polarity.Anna Szabolcsi - 2004 - Natural Language and Linguistic Theory 22 (2):409-452..
    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 (...)
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  • Extended Syllogistics in Calculus CL.Jens Lemanski - 2020 - Journal of Applied Logics 8 (2):557-577.
    Extensions of traditional syllogistics have been increasingly researched in philosophy, linguistics, and areas such as artificial intelligence and computer science in recent decades. This is mainly due to the fact that syllogistics is seen as a logic that comes very close to natural language abilities. Various forms of extended syllogistics have become established. This paper deals with the question to what extent a syllogistic representation in CL diagrams can be seen as a form of extended syllogistics. It will be shown (...)
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  • Learnability and Semantic Universals.Shane Steinert-Threlkeld & Jakub Szymanik - forthcoming - Semantics and Pragmatics.
    One of the great successes of the application of generalized quantifiers to natural language has been the ability to formulate robust semantic universals. When such a universal is attested, the question arises as to the source of the universal. In this paper, we explore the hypothesis that many semantic universals arise because expressions satisfying the universal are easier to learn than those that do not. While the idea that learnability explains universals is not new, explicit accounts of learning that can (...)
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  • Conservativity: a necessary property for the maximization of witness sets.L. Robaldo - 2013 - Logic Journal of the IGPL 21 (5):853-878.
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  • Far from obvious: the semantics of locative indefinites.Sela Mador-Haim & Yoad Winter - 2015 - Linguistics and Philosophy 38 (5):437-476.
    Simple locative sentences show a variety of pseudo-quantificational interpretations. Some locatives give the impression of universal quantification over parts of objects, others involve existential quantification, and yet others cannot be characterized by either of these quantificational terms. This behavior is explained by virtually all semantic theories of locatives. What has not been previously observed is that similar quantificational variability is also exhibited by locative sentences containing indefinites with the ‘a’ article. This phenomenon is especially problematic for traditional existential treatments of (...)
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  • Iterating semantic automata.Shane Steinert-Threlkeld & I. I. I. Thomas F. Icard - 2013 - Linguistics and Philosophy 36 (2):151-173.
    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 (...)
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  • An intensional parametric semantics for vague quantifiers.Shalom Lappin - 2000 - Linguistics and Philosophy 23 (6):599-620.
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  • Kvantifikácia v prirodzenom jazyku (III).Marián Zouhar - 2006 - Organon F: Medzinárodný Časopis Pre Analytickú Filozofiu 13 (4):379-394.
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  • Bare Quantifiers.Zoltán Gendler Szabó - 2011 - Philosophical Review 120 (2):247-283.
    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 (...)
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  • (1 other version)Deixis and Anaphora.François Recanati - 2004 - In Zoltan Gendler Szabo (ed.), Semantics Versus Pragmatics. Oxford, GB: Oxford University Press UK. pp. 286--316.
    A defence of the 'pragmatic' theory of anaphora (which stresses the analogy between anaphora and deixis) against an argument put forward by Gareth Evans.
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