Search results for 'quantifiers' (try it on Scholar)

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  1. Noun Phrases & Generalized Quantifiers (1987). Jon Barwise. In Peter Gärdenfors (ed.), Generalized Quantifiers. Reidel Publishing Company 31--1.
     
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  2. Branching Generalized Quantifiers (1987). Dag Westerstahl. In Peter Gärdenfors (ed.), Generalized Quantifiers. Reidel Publishing Company 269.
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  3.  70
    Stanley Peters & Dag Westersthl (2006). Quantifiers in Language and Logic. 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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  4. Peter Fritz (2013). Modal Ontology and Generalized Quantifiers. 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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  5.  19
    Martin Hackl (2009). On the Grammar and Processing of Proportional Quantifiers: Most Versus More Than Half. [REVIEW] 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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  6.  45
    Jakub Szymanik (2009). Quantifiers in TIME and SPACE. Computational Complexity of Generalized Quantifiers in Natural Language. 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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  7. Joanna Golinska-Pilarek & Konrad Zdanowski (2003). Spectra of Formulae with Henkin Quantifiers. 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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  8.  26
    Fredrik Engström (2012). Generalized Quantifiers in Dependence Logic. 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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  9.  56
    Jakub Szymanik (2010). Computational Complexity of Polyadic Lifts of Generalized Quantifiers in Natural Language. 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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  10.  52
    Friederike Moltmann (2003). Nominalizing Quantifiers. 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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  11.  51
    Bart Geurts (2003). Reasoning with Quantifiers. 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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  12.  8
    V. Troiani, J. Peelle, R. Clark & M. Grossman (2009). Is It Logical to Count on Quantifiers? Dissociable Neural Networks Underlying Numerical and Logical Quantifiers. 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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  13.  32
    Marcin Zajenkowski, Rafał Styła & Jakub Szymanik (2011). A Computational Approach to Quantifiers as an Explanation for Some Language Impairments in Schizophrenia. 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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  14.  34
    Reiner Hähnle (1998). Commodious Axiomatization of Quantifiers in Multiple-Valued Logic. 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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  15.  58
    Jakub Szymanik & Marcin Zajenkowski (2010). Quantifiers and Working Memory. 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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  16.  40
    Jakub Szymanik & Marcin Zajenkowski (2009). Comprehension of Simple Quantifiers. Empirical Evaluation of a Computational Model. Cognitive Science: A Multidisciplinary Journal 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.
    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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  17.  17
    Livio Robaldo (2010). Independent Set Readings and Generalized Quantifiers. 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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  18.  10
    Ariel Cohen & Manfred Krifka (2014). Superlative Quantifiers and Meta-Speech Acts. 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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  19.  49
    Marcin Mostowski & Jakub Szymanik (2007). Computational Complexity of Some Ramsey Quantifiers in Finite Models. 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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  20.  44
    Wiebe Van Der Hoek & Maarten De Rijke (1993). Generalized Quantifiers and Modal Logic. 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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  21.  34
    Marcin Mostowski (1998). Computational Semantics for Monadic Quantifiers. 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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  22.  33
    Juha Kontinen & Jakub Szymanik (2011). Characterizing Definability of Second-Order Generalized Quantifiers. 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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  23.  59
    Jeffrey C. King (2008). Complex Demonstratives as Quantifiers: Objections and Replies. 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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  24.  9
    Alessandro Torza (2015). Necessarily Maybe. Quantifiers, Modality and Vagueness. In Quantifiers, Quantifiers, and Quantifiers. Themes in Logic, Metaphysics and Language. (Synthese Library vol 373). Springer 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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  25.  13
    Maria Spychalska (forthcoming). At Least Not False, at Most Possible: Between Truth and Assertibility of Superlative Quantifiers. Synthese:1-32.
    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 (...)
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  26.  34
    Hanoch Ben-Yami (2009). Generalized Quantifiers, and Beyond. 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.  15
    Marcin Mostowski & Konrad Zdanowski (2004). Degrees of Logics with Henkin Quantifiers in Poor Vocabularies. Archive for Mathematical Logic 43 (5):691-702.
    We investigate some logics with Henkin quantifiers. For a given logic L, we consider questions of the form: what is the degree of the set of L–tautologies in a poor vocabulary (monadic or empty)? We prove that the set of tautologies of the logic with all Henkin quantifiers in empty vocabulary L*∅ is of degree 0’. We show that the same holds also for some weaker logics like L ∅(Hω) and L ∅(Eω). We show that each logic of (...)
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  28.  76
    Ken Akiba (2009). A New Theory of Quantifiers and Term Connectives. Journal of Logic, Language and Information 18 (3):403-431.
    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 (...)
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  29.  26
    Anthony J. Sanford, Linda M. Moxey & Kevin Paterson (1994). Psychological Studies of Quantifiers. 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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  30.  39
    Jouko Väänänen & Dag Westerståhl (2002). On the Expressive Power of Monotone Natural Language Quantifiers Over Finite Models. 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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  31.  40
    Tapani Hyttinen & Gabriel Sandu (2000). Henkin Quantifiers and the Definability of Truth. 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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  32.  19
    John Nerbonne (1995). Nominal Comparatives and Generalized Quantifiers. 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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  33.  22
    Lauri Hella, Jouko Väänänen & Dag Westerståhl (1997). Definability of Polyadic Lifts of Generalized Quantifiers. 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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  34.  6
    Sailee Shikhare, Stefan Heim, Elise Klein, Stefan Huber & Klaus Willmes (2015). Processing of Numerical and Proportional Quantifiers. 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.  19
    Nissim Francez (2014). A Logic Inspired by Natural Language: Quantifiers As Subnectors. 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.  11
    Blanka Kozlíková & Vítězslav Švejdar (2006). On Interplay of Quantifiers in Gödel-Dummett Fuzzy Logics. Archive for Mathematical Logic 45 (5):569-580.
    Axiomatization of Gödel-Dummett predicate logics S2G, S3G, and PG, where PG is the weakest logic in which all prenex operations are sound, and the relationships of these logics to logics known from the literature are discussed. Examples of non-prenexable formulas are given for those logics where some prenex operation is not available. Inter-expressibility of quantifiers is explored for each of the considered logics.
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  37.  7
    Franco Montagna (2012). Δ-Core Fuzzy Logics with Propositional Quantifiers, Quantifier Elimination and Uniform Craig Interpolation. 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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  38.  20
    Ian Pratt-Hartmann (2005). Complexity of the Two-Variable Fragment with Counting Quantifiers. 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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  39.  2
    Vincenzo Moscati, Jacopo Romoli, Tommaso Federico Demarie & Stephen Crain (2016). Born in the USA: A Comparison of Modals and Nominal Quantifiers in Child Language. Natural Language Semantics 24 (1):79-115.
    One of the challenges confronted by language learners is to master the interpretation of sentences with multiple logical operators, where different interpretations depend on different scope assignments. Five-year-old children have been found to access some readings of potentially ambiguous sentences much less than adults do :73–102, 2006; Musolino, Universal Grammar and the acquisition of semantic knowledge, 1998; Musolino and Lidz, Lang Acquis 11:277–291, 2003, among many others). Recently, Gualmini et al. have shown that, by careful contextual manipulation, it is possible (...)
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  40.  11
    R. Zuber (2007). Symmetric and Contrapositional Quantifiers. 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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  41.  3
    Juha Kontinen (2004). Definability of Second Order Generalized Quantifiers. 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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  42.  17
    Jouko Väänänen (1997). Unary Quantifiers on Finite Models. 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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  43.  1
    Petra Murinová & Vilém Novák (2016). Syllogisms and 5-Square of Opposition with Intermediate Quantifiers in Fuzzy Natural Logic. Logica Universalis 10 (2-3):339-357.
    In this paper, we provide an overview of some of the results obtained in the mathematical theory of intermediate quantifiers that is part of fuzzy natural logic. We briefly introduce the mathematical formal system used, the general definition of intermediate quantifiers and define three specific ones, namely, “Almost all”, “Most” and “Many”. Using tools developed in FNL, we present a list of valid intermediate syllogisms and analyze a generalized 5-square of opposition.
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  44. Jakub Szymanik & Marcin Zajenkowski (2009). Understanding Quantifiers in Language. In N. A. Taatgen & H. van Rijn (eds.), Proceedings of the 31st Annual Conference of the Cognitive Science Society.
    We compare time needed for understanding different types of quantifiers. We show that the computational distinction between quantifiers recognized by finite-automata and pushdown automata is psychologically relevant. Our research improves upon hypothesis and explanatory power of recent neuroimaging studies as well as provides evidence for the claim that human linguistic abilities are constrained by computational complexity.
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  45.  28
    Jakub Szymanik (2010). Almost All Complex Quantifiers Are Simple. In C. Ebert, G. Jäger, M. Kracht & J. Michaelis (eds.), Mathematics of Language 10/11, Lecture Notes in Computer Science 6149. Springer
    We prove that PTIME generalized quantifiers are closed under Boolean operations, iteration, cumulation and resumption. -/- .
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  46.  8
    Lauri Hella & Juha Nurmonen (2000). Vectorization Hierarchies of Some Graph Quantifiers. Archive for Mathematical Logic 39 (3):183-207.
    We give a sufficient condition for the inexpressibility of the k-th extended vectorization of a generalized quantifier $\sf Q$ in ${\rm FO}({\vec Q}_k)$ , the extension of first-order logic by all k-ary quantifiers. The condition is based on a model construction which, given two ${\rm FO}({\vec Q}_1)$ -equivalent models with certain additional structure, yields a pair of ${\rm FO}({\vec Q}_k)$ -equivalent models. We also consider some applications of this condition to quantifiers that correspond to graph properties, such as (...)
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  47.  30
    Dorit Ben Shalom (2003). One Connection Between Standard Invariance Conditions on Modal Formulas and Generalized Quantifiers. Journal of Logic, Language and Information 12 (1):47-52.
    The language of standard propositional modal logic has one operator (? or ?), that can be thought of as being determined by the quantifiers ? or ?, respectively: for example, a formula of the form ?F is true at a point s just in case all the immediate successors of s verify F.This paper uses a propositional modal language with one operator determined by a generalized quantifier to discuss a simple connection between standard invariance conditions on modal formulas and (...)
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  48.  26
    Edward Keenan & Denis Paperno (2010). Stanley Peters and Dag Westerståhl: Quantifiers in Language and Logic. [REVIEW] Linguistics and Philosophy 33 (6):513-549.
    Quantifiers in Language and Logic (QLL) is a major contribution to natural language semantics, specifically to quantification. It integrates the extensive recent work on quantifiers in logic and linguistics. It also presents new observations and results. QLL should help linguists understand the mathematical generalizations we can make about natural language quantification, and it should interest logicians by presenting an extensive array of quantifiers that lie beyond the pale of classical logic. Here we focus on those aspects of (...)
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  49.  4
    Antti Kuusisto (2015). A Double Team Semantics for Generalized Quantifiers. 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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  50.  7
    Steffen Lewitzka (2015). Denotational Semantics for Modal Systems S3–S5 Extended by Axioms for Propositional Quantifiers and Identity. Studia Logica 103 (3):507-544.
    There are logics where necessity is defined by means of a given identity connective: \ is a tautology). On the other hand, in many standard modal logics the concept of propositional identity \ can be defined by strict equivalence \}\). All these approaches to modality involve a principle that we call the Collapse Axiom : “There is only one necessary proposition.” In this paper, we consider a notion of PI which relies on the identity axioms of Suszko’s non-Fregean logic SCI. (...)
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