Results for 'Reducible quantifiers'

998 found
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  1.  24
    A Note on the Monotonicity of Reducible Quantifiers.R. Zuber - 2010 - Journal of Logic, Language and Information 19 (1):123-128.
    We provide necessary and sufficient conditions determining how monotonicity of some classes of reducible quantifiers depends on the monotonicity of simpler quantifiers of iterations to which they are equivalent.
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  2. Jon Barwise.Noun Phrases & Generalized Quantifiers - 1987 - In Peter Gärdenfors (ed.), Generalized Quantifiers. Reidel Publishing Company. pp. 31--1.
     
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  3. Dag Westerstahl.Branching Generalized Quantifiers - 1987 - In Peter Gärdenfors (ed.), Generalized Quantifiers. Reidel Publishing Company. pp. 269.
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  4.  42
    Natural Language, Sortal Reducibility and Generalized Quantifiers.Edward L. Keenan - 1993 - Journal of Symbolic Logic 58 (1):314-325.
    Recent work in natural language semantics leads to some new observations on generalized quantifiers. In § 1 we show that English quantifiers of type $ $ are booleanly generated by their generalized universal and generalized existential members. These two classes also constitute the sortally reducible members of this type. Section 2 presents our main result--the Generalized Prefix Theorem (GPT). This theorem characterizes the conditions under which formulas of the form Q1x 1⋯ Qnx nRx 1⋯ xn and q1x (...)
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  5.  91
    Quantifiers in Language and Logic.Stanley Peters & Dag Westersthl - 2006 - Clarendon Press.
    Quantification is a topic which brings together linguistics, logic, and philosophy. Quantifiers are the essential tools with which, in language or logic, we refer to quantity of things or amount of stuff. In English they include such expressions as no, some, all, both, many. Peters and Westerstahl present the definitive interdisciplinary exploration of how they work - their syntax, semantics, and inferential role.
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  6.  38
    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 (...)
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  7.  83
    Comprehension of Simple Quantifiers: Empirical Evaluation of a Computational Model.Jakub Szymanik & Marcin Zajenkowski - 2010 - Cognitive Science 34 (3):521-532.
    We examine the verification of simple quantifiers in natural language from a computational model perspective. We refer to previous neuropsychological investigations of the same problem and suggest extending their experimental setting. Moreover, we give some direct empirical evidence linking computational complexity predictions with cognitive reality.<br>In the empirical study we compare time needed for understanding different types of quantifiers. We show that the computational distinction between quantifiers recognized by finite-automata and push-down automata is psychologically relevant. Our research improves (...)
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  8.  15
    Categories of First -Order Quantifiers.Urszula Wybraniec-Skardowska - 2018 - Lvov-Warsaw School. Past and Present.
    One well known problem regarding quantifiers, in particular the 1st order quantifiers, is connected with their syntactic categories and denotations.The unsatisfactory efforts to establish the syntactic and ontological categories of quantifiers in formalized first-order languages can be solved by means of the so called principle of categorial compatibility formulated by Roman Suszko, referring to some innovative ideas of Gottlob Frege and visible in syntactic and semantic compatibility of language expressions. In the paper the principle is introduced for (...)
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  9. Generalized Quantifiers and Natural Language.John Barwise & Robin Cooper - 1981 - Linguistics and Philosophy 4 (2):159--219.
  10. Quantifiers and Epistemic Contextualism.Jonathan Ichikawa - 2011 - Philosophical Studies 155 (3):383-398.
    I defend a neo-Lewisean form of contextualism about knowledge attributions. Understanding the context-sensitivity of knowledge attributions in terms of the context-sensitivity of universal quantifiers provides an appealing approach to knowledge. Among the virtues of this approach are solutions to the skeptical paradox and the Gettier problem. I respond to influential objections to Lewis’s account.
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  11. Modal Ontology and Generalized Quantifiers.Peter Fritz - 2013 - Journal of Philosophical Logic 42 (4):643-678.
    Timothy Williamson has argued that in the debate on modal ontology, the familiar distinction between actualism and possibilism should be replaced by a distinction between positions he calls contingentism and necessitism. He has also argued in favor of necessitism, using results on quantified modal logic with plurally interpreted second-order quantifiers showing that necessitists can draw distinctions contingentists cannot draw. Some of these results are similar to well-known results on the relative expressivity of quantified modal logics with so-called inner and (...)
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  12.  55
    Quantifiers in TIME and SPACE. Computational Complexity of Generalized Quantifiers in Natural Language.Jakub Szymanik - 2009 - Dissertation, University of Amsterdam
    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 (...)
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  13.  79
    Nominalizing Quantifiers.Friederike Moltmann - 2003 - Journal of Philosophical Logic 32 (5):445-481.
    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 (...)
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  14.  11
    Is It Logical to Count on Quantifiers? Dissociable Neural Networks Underlying Numerical and Logical Quantifiers.V. Troiani, J. Peelle, R. Clark & M. Grossman - 2009 - Neuropsychologia 47 (1):104--111.
    The present study examined the neural substrate of two classes of quantifiers: numerical quantifiers like ” at least three” which require magnitude processing, and logical quantifiers like ” some” which can be understood using a simple form of perceptual logic. We assessed these distinct classes of quantifiers with converging observations from two sources: functional imaging data from healthy adults, and behavioral and structural data from patients with corticobasal degeneration who have acalculia. Our findings are consistent with (...)
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  15.  78
    Computational Complexity of Polyadic Lifts of Generalized Quantifiers in Natural Language.Jakub Szymanik - 2010 - Linguistics and Philosophy 33 (3):215-250.
    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 (...)
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  16.  36
    Generalized Quantifiers in Dependence Logic.Fredrik Engström - 2012 - Journal of Logic, Language and Information 21 (3):299-324.
    We introduce generalized quantifiers, as defined in Tarskian semantics by Mostowski and Lindström, in logics whose semantics is based on teams instead of assignments, e.g., IF-logic and Dependence logic. Both the monotone and the non-monotone case is considered. It is argued that to handle quantifier scope dependencies of generalized quantifiers in a satisfying way the dependence atom in Dependence logic is not well suited and that the multivalued dependence atom is a better choice. This atom is in fact (...)
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  17.  67
    Quantification and the Nature of Crosslinguistic Variation.Lisa Matthewson - 2001 - Natural Language Semantics 9 (2):145-189.
    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 (...)
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  18.  83
    Reasoning with Quantifiers.Bart Geurts - 2003 - Cognition 86 (3):223--251.
    In the semantics of natural language, quantification may have received more attention than any other subject, and one of the main topics in psychological studies on deductive reasoning is syllogistic inference, which is just a restricted form of reasoning with quantifiers. But thus far the semantical and psychological enterprises have remained disconnected. This paper aims to show how our understanding of syllogistic reasoning may benefit from semantical research on quantification. I present a very simple logic that pivots on the (...)
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  19.  35
    Categories of First-Order Quantifiers.Urszula Wybraniec-Skardowska - 2018 - In Urszula Wybraniec-Skardowska & Ángel Garrido (eds.), The Lvov-Warsaw School. Past and Present. Basel, Switzerland: pp. 575-597.
    One well known problem regarding quantifiers, in particular the 1storder quantifiers, is connected with their syntactic categories and denotations. The unsatisfactory efforts to establish the syntactic and ontological categories of quantifiers in formalized first-order languages can be solved by means of the so called principle of categorial compatibility formulated by Roman Suszko, referring to some innovative ideas of Gottlob Frege and visible in syntactic and semantic compatibility of language expressions. In the paper the principle is introduced for (...)
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  20.  11
    A Double Team Semantics for Generalized Quantifiers.Antti Kuusisto - 2015 - Journal of Logic, Language and Information 24 (2):149-191.
    We investigate extensions of dependence logic with generalized quantifiers. We also introduce and investigate the notion of a generalized atom. We define a system of semantics that can accommodate variants of dependence logic, possibly extended with generalized quantifiers and generalized atoms, under the same umbrella framework. The semantics is based on pairs of teams, or double teams. We also devise a game-theoretic semantics equivalent to the double team semantics. We make use of the double team semantics by defining (...)
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  21.  32
    Independent Set Readings and Generalized Quantifiers.Livio Robaldo - 2010 - Journal of Philosophical Logic 39 (1):23-58.
    Several authors proposed to devise logical structures for Natural Language (NL) semantics in which noun phrases yield referential terms rather than standard Generalized Quantifiers. In this view, two main problems arise: the need to refer to the maximal sets of entities involved in the predications and the need to cope with Independent Set (IS) readings, where two or more sets of entities are introduced in parallel. The article illustrates these problems and their consequences, then presents an extension of the (...)
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  22. Spectra of Formulae with Henkin Quantifiers.Joanna Golinska-Pilarek & Konrad Zdanowski - 2003 - In A. Rojszczak, J. Cachro & G. Kurczewski (eds.), Philosophical Dimensions of Logic and Science. Kluwer Academic Publishers.
    It is known that various complexity-theoretical problems can be translated into some special spectra problems. Thus, questions about complexity classes are translated into questions about the expressive power of some languages. In this paper we investigate the spectra of some logics with Henkin quantifiers in the empty vocabulary.
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  23.  51
    Nonexistent Objects as Truth-Makers: Against Crane’s Reductionism.Filippo Casati & Naoya Fujikawa - 2016 - Philosophia 44 (2):423-434.
    According to Meinongianism, some objects do not exist but we can legitimately refer to and quantify over them. Moreover, Meinongianism standardly regards nonexistent objects as contributing to the truth-makers of sentences about nonexistent objects. Recently, Tim Crane has proposed a weak form of Meinongianism, a reductionism, which denies any contribution of nonexistent objects to truth-making. His reductionism claims that, even though we can truly talk about nonexistent objects by using singular terms and quantifiers about them, any truth about nonexistent (...)
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  24.  27
    Superlative Quantifiers and Meta-Speech Acts.Ariel Cohen & Manfred Krifka - 2014 - Linguistics and Philosophy 37 (1):41-90.
    Recent research has shown that the superlative quantifiers at least and at most do not have the same type of truth conditions as the comparative quantifiers more than and fewer than. We propose that superlative quantifiers are interpreted at the level of speech acts. We relate them to denegations of speech acts, as in I don’t promise to come, which we analyze as excluding the speech act of a promise to come. Calling such conversational acts that affect (...)
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  25.  42
    A Computational Approach to Quantifiers as an Explanation for Some Language Impairments in Schizophrenia.Marcin Zajenkowski, Rafał Styła & Jakub Szymanik - 2011 - Journal of Communication Disorder 44:2011.
    We compared the processing of natural language quantifiers in a group of patients with schizophrenia and a healthy control group. In both groups, the difficulty of the quantifiers was consistent with computational predictions, and patients with schizophrenia took more time to solve the problems. However, they were significantly less accurate only with proportional quantifiers, like more than half. This can be explained by noting that, according to the complexity perspective, only proportional quantifiers require working memory engagement.
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  26.  55
    Generalized Quantifiers, and Beyond.Hanoch Ben-Yami - 2009 - Logique Et Analyse (208):309-326.
    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.
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  27.  86
    Complex Demonstratives as Quantifiers: Objections and Replies.Jeffrey C. King - 2008 - Philosophical Studies 141 (2):209-242.
    In “Complex Demonstratives: A Quantificational Account” (MIT Press 2001) (henceforth CD), I argued that complex demonstratives are quantifiers. Many philosophers had held that demonstratives, both simple and complex, are referring terms. Since the publication of CD various objections to the account of complex demonstratives I defended in it have been raised. In the present work, I lay out these objections and respond to them.
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  28.  66
    Generalized Quantifiers and Modal Logic.Wiebe Van Der Hoek & Maarten De Rijke - 1993 - Journal of Logic, Language and Information 2 (1):19-58.
    We study several modal languages in which some (sets of) generalized quantifiers can be represented; the main language we consider is suitable for defining any first order definable quantifier, but we also consider a sublanguage thereof, as well as a language for dealing with the modal counterparts of some higher order quantifiers. These languages are studied both from a modal logic perspective and from a quantifier perspective. Thus the issues addressed include normal forms, expressive power, completeness both of (...)
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  29.  26
    Necessarily Maybe. Quantifiers, Modality and Vagueness.Alessandro Torza - 2015 - In Quantifiers, Quantifiers, and Quantifiers. Themes in Logic, Metaphysics and Language. (Synthese Library vol 373). Springer. pp. 367-387.
    Languages involving modalities and languages involving vagueness have each been thoroughly studied. On the other hand, virtually nothing has been said about the interaction of modality and vagueness. This paper aims to start filling that gap. Section 1 is a discussion of various possible sources of vague modality. Section 2 puts forward a model theory for a quantified language with operators for modality and vagueness. The model theory is followed by a discussion of the resulting logic. In Section 3, the (...)
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  30.  27
    At Least Not False, at Most Possible: Between Truth and Assertibility of Superlative Quantifiers.Maria Spychalska - 2018 - Synthese 195 (2):571-602.
    Generalized Quantifier Theory defines superlative quantifiers at most n and at least n as truth-conditionally equivalent to comparative quantifiers fewer than n+1 and more than n \1. It has been demonstrated, however, that this standard theory cannot account for various linguistic differences between these two types of quantifiers. In this paper I discuss how the distinction between assertibility and truth-conditions can be applied to explain this phenomenon. I draw a parallel between the assertibility of disjunctions and superlative (...)
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  31.  64
    Quantifiers and Working Memory.Jakub Szymanik & Marcin Zajenkowski - 2010 - In Maria Aloni & Katrin Schulz (eds.), Amsterdam Colloquium 2009, LNAI 6042. Springer.
    The paper presents a study examining the role of working<br>memory in quantifier verification. We created situations similar to the<br>span task to compare numerical quantifiers of low and high rank, parity<br>quantifiers and proportional quantifiers. The results enrich and support<br>the data obtained previously in and predictions drawn from a computational<br>model.
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  32.  46
    Computational Semantics for Monadic Quantifiers.Marcin Mostowski - 1998 - Journal of Applied Non--Classical Logics 8 (1-2):107--121.
    The paper gives a survey of known results related to computational devices (finite and push–down automata) recognizing monadic generalized quantifiers in finite models. Some of these results are simple reinterpretations of descriptive—feasible correspondence theorems from finite–model theory. Additionally a new result characterizing monadic quantifiers recognized by push down automata is proven.
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  33.  38
    Psychological Studies of Quantifiers.Anthony J. Sanford, Linda M. Moxey & Kevin Paterson - 1994 - Journal of Semantics 11 (3):153-170.
    In this paper we present a summary review of recent psychological studies which make a contribution to an understanding of how quantifiers are used. Until relatively recently, the contribution which psychology has made has been somewhat restricted. For example, the approach which has enjoyed the greatest popularity in psychology is explaining quantifiers as expressions which have fuzzy or vague projections on to mental scales of amount. Following Moxey & Sanford (1993a), this view is questioned. Experimental work is summarized (...)
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  34.  12
    Processing of Numerical and Proportional Quantifiers.Sailee Shikhare, Stefan Heim, Elise Klein, Stefan Huber & Klaus Willmes - 2015 - Cognitive Science 39 (7):1504-1536.
    Quantifier expressions like “many” and “at least” are part of a rich repository of words in language representing magnitude information. The role of numerical processing in comprehending quantifiers was studied in a semantic truth value judgment task, asking adults to quickly verify sentences about visual displays using numerical or proportional quantifiers. The visual displays were composed of systematically varied proportions of yellow and blue circles. The results demonstrated that numerical estimation and numerical reference information are fundamental in encoding (...)
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  35.  29
    A Logic Inspired by Natural Language: Quantifiers As Subnectors.Nissim Francez - 2014 - Journal of Philosophical Logic 43 (6):1153-1172.
    Inspired by the grammar of natural language, the paper presents a variant of first-order logic, in which quantifiers are not sentential operators, but are used as subnectors . A quantified term formed by a subnector is an argument of a predicate. The logic is defined by means of a meaning-conferring natural-deduction proof-system, according to the proof-theoretic semantics program. The harmony of the I/E-rules is shown. The paper then presents a translation, called the Frege translation, from the defined logic to (...)
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  36.  30
    Complexity of the Two-Variable Fragment with Counting Quantifiers.Ian Pratt-Hartmann - 2005 - Journal of Logic, Language and Information 14 (3):369-395.
    The satisfiability and finite satisfiability problems for the two-variable fragment of first-order logic with counting quantifiers are both in NEXPTIME, even when counting quantifiers are coded succinctly.
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  37.  65
    Computational Complexity of Some Ramsey Quantifiers in Finite Models.Marcin Mostowski & Jakub Szymanik - 2007 - Bulletin of Symbolic Logic 13:281--282.
    The problem of computational complexity of semantics for some natural language constructions – considered in [M. Mostowski, D. Wojtyniak 2004] – motivates an interest in complexity of Ramsey quantifiers in finite models. In general a sentence with a Ramsey quantifier R of the following form Rx, yH(x, y) is interpreted as ∃A(A is big relatively to the universe ∧A2 ⊆ H). In the paper cited the problem of the complexity of the Hintikka sentence is reduced to the problem of (...)
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  38.  53
    Definability of Polyadic Lifts of Generalized Quantifiers.Lauri Hella, Jouko Väänänen & Dag Westerståhl - 1997 - Journal of Logic, Language and Information 6 (3):305-335.
    We study generalized quantifiers on finite structures.With every function : we associate a quantifier Q by letting Q x say there are at least (n) elementsx satisfying , where n is the sizeof the universe. This is the general form ofwhat is known as a monotone quantifier of type .We study so called polyadic liftsof such quantifiers. The particular lifts we considerare Ramseyfication, branching and resumption.In each case we get exact criteria fordefinability of the lift in terms of (...)
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  39.  23
    Nominal Comparatives and Generalized Quantifiers.John Nerbonne - 1995 - Journal of Logic, Language and Information 4 (4):273-300.
    This work adopts the perspective of plural logic and measurement theory in order first to focus on the microstructure of comparative determiners; and second, to derive the properties of comparative determiners as these are studied in Generalized Quantifier Theory, locus of the most sophisticated semantic analysis of natural language determiners. The work here appears to be the first to examine comparatives within plural logic, a step which appears necessary, but which also harbors specific analytical problems examined here.Since nominal comparatives involve (...)
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  40.  5
    Definability of Second Order Generalized Quantifiers.Juha Kontinen - 2004 - Dissertation,
    We study second order generalized quantifiers on finite structures. One starting point of this research has been the notion of definability of Lindström quantifiers. We formulate an analogous notion for second order generalized quantifiers and study definability of second order generalized quantifiers in terms of Lindström quantifiers.
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  41.  45
    Unary Quantifiers on Finite Models.Jouko Väänänen - 1997 - Journal of Logic, Language and Information 6 (3):275-304.
    In this paper (except in Section 5) all quantifiers are assumedto be so called simple unaryquantifiers, and all models are assumedto be finite. We give a necessary and sufficientcondition for a quantifier to be definablein terms of monotone quantifiers. For amonotone quantifier we give a necessaryand sufficient condition for beingdefinable in terms of a given set of bounded monotonequantifiers. Finally, we give a necessaryand sufficient condition for a monotonequantifier to be definable in terms of agiven monotone quantifier.Our analysis (...)
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  42.  44
    Characterizing Definability of Second-Order Generalized Quantifiers.Juha Kontinen & Jakub Szymanik - 2011 - In L. Beklemishev & R. de Queiroz (eds.), Proceedings of the 18th Workshop on Logic, Language, Information and Computation, Lecture Notes in Artificial Intelligence 6642. Springer.
    We study definability of second-order generalized quantifiers. We show that the question whether a second-order generalized quantifier $\sQ_1$ is definable in terms of another quantifier $\sQ_2$, the base logic being monadic second-order logic, reduces to the question if a quantifier $\sQ^{\star}_1$ is definable in $\FO(\sQ^{\star}_2,<,+,\times)$ for certain first-order quantifiers $\sQ^{\star}_1$ and $\sQ^{\star}_2$. We use our characterization to show new definability and non-definability results for second-order generalized quantifiers. In particular, we show that the monadic second-order majority quantifier $\most^1$ (...)
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  43.  51
    On the Expressive Power of Monotone Natural Language Quantifiers Over Finite Models.Jouko Väänänen & Dag Westerståhl - 2002 - Journal of Philosophical Logic 31 (4):327-358.
    We study definability in terms of monotone generalized quantifiers satisfying Isomorphism Closure, Conservativity and Extension. Among the quantifiers with the latter three properties - here called CE quantifiers - one finds the interpretations of determiner phrases in natural languages. The property of monotonicity is also linguistically ubiquitous, though some determiners like an even number of are highly non-monotone. They are nevertheless definable in terms of monotone CE quantifiers: we give a necessary and sufficient condition for such (...)
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  44.  58
    Henkin Quantifiers and the Definability of Truth.Tapani Hyttinen & Gabriel Sandu - 2000 - Journal of Philosophical Logic 29 (5):507-527.
    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 (...)
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  45.  14
    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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  46.  15
    Δ-Core Fuzzy Logics with Propositional Quantifiers, Quantifier Elimination and Uniform Craig Interpolation.Franco Montagna - 2012 - Studia Logica 100 (1-2):289-317.
    In this paper we investigate the connections between quantifier elimination, decidability and Uniform Craig Interpolation in Δ-core fuzzy logics added with propositional quantifiers. As a consequence, we are able to prove that several propositional fuzzy logics have a conservative extension which is a Δ-core fuzzy logic and has Uniform Craig Interpolation.
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  47.  26
    Meanwhile, Within the Frege Boundary.Paul Dekker - 2003 - Linguistics and Philosophy 26 (5):547-556.
    In this paper, I want to contribute to understanding and improving on Keenan'sintriguing equivalence result about reducible type quantifiers (Keenan, 1992).I give an alternative proof of his result which generalizes to type quantifiers, andI show how the reduction of a reducible type quantifier to (the composition of) ntype quantifiers can be effected.
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  48.  44
    Commodious Axiomatization of Quantifiers in Multiple-Valued Logic.Reiner Hähnle - 1998 - Studia Logica 61 (1):101-121.
    We provide tools for a concise axiomatization of a broad class of quantifiers in many-valued logic, so-called distribution quantifiers. Although sound and complete axiomatizations for such quantifiers exist, their size renders them virtually useless for practical purposes. We show that for quantifiers based on finite distributive lattices compact axiomatizations can be obtained schematically. This is achieved by providing a link between skolemized signed formulas and filters/ideals in Boolean set lattices. Then lattice theoretic tools such as Birkhoff's (...)
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  49.  11
    Generalized Quantifiers and Modal Logic.Wiebe Hoek & Maarten Rijke - 1993 - Journal of Logic, Language and Information 2 (1):19-58.
    We study several modal languages in which some (sets of) generalized quantifiers can be represented; the main language we consider is suitable for defining any first order definable quantifier, but we also consider a sublanguage thereof, as well as a language for dealing with the modal counterparts of some higher order quantifiers. These languages are studied both from a modal logic perspective and from a quantifier perspective. Thus the issues addressed include normal forms, expressive power, completeness both of (...)
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  50.  62
    The Square of Opposition and Generalized Quantifiers.Duilio D'Alfonso - 2012 - In J.-Y. Beziau & Dale Jacquette (eds.), Around and Beyond the Square of Opposition. Birkhäuser. pp. 219--227.
    In this paper I propose a set-theoretical interpretation of the logical square of opposition, in the perspective opened by generalized quantifier theory. Generalized quantifiers allow us to account for the semantics of quantificational Noun Phrases, and of other natural language expressions, in a coherent and uniform way. I suggest that in the analysis of the meaning of Noun Phrases and Determiners the square of opposition may help representing some semantic features responsible to different logical properties of these expressions. I (...)
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