Results for 'generalized quantifier'

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  1.  17
    'Only' as a Determiner and as a Generalized Quantifier.Sjaak de Mey - 1991 - Journal of Semantics 8 (1-2):91-106.
    Two types of linguistic theories have been particularly concerned with the analysis of ‘only’: pragmatics, in particular focus theory and presupposition theory, and generalized quantifier (GQ) theory, the latter in the negative sense that it has been eager to show that ‘only’ is not a GQ. Judging from such analyses, then, it would appear that the analysis of ‘only’ is not at home in the grammar of natural language. The main negative point of the present article is to (...)
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  2.  10
    Generalized Quantifier and a Bounded Arithmetic Theory for LOGCFL.Satoru Kuroda - 2007 - Archive for Mathematical Logic 46 (5-6):489-516.
    We define a theory of two-sort bounded arithmetic whose provably total functions are exactly those in ${\mathcal{F}_{LOGCFL}}$ by way of a generalized quantifier that expresses computations of SAC 1 circuits. The proof depends on Kolokolova’s conditions for the connection between the provable capture in two-sort theories and descriptive complexity.
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  3.  46
    On a Decidable Generalized Quantifier Logic Corresponding to a Decidable Fragment of First-Order Logic.Natasha Alechina - 1995 - Journal of Logic, Language and Information 4 (3):177-189.
    Van Lambalgen (1990) proposed a translation from a language containing a generalized quantifierQ into a first-order language enriched with a family of predicatesR i, for every arityi (or an infinitary predicateR) which takesQxg(x, y1,..., yn) to x(R(x, y1,..., y1) (x,y1,...,yn)) (y 1,...,yn are precisely the free variables ofQx). The logic ofQ (without ordinary quantifiers) corresponds therefore to the fragment of first-order logic which contains only specially restricted quantification. We prove that it is decidable using the method of analytic tableaux. (...)
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  4.  5
    Natural Language and Generalized Quantifier Theory.Sebastian Löbner - 1987 - In Peter Gärdenfors (ed.), Generalized Quantifiers. Reidel Publishing Company. pp. 181--201.
  5.  40
    Some Properties of Natural Language Quantifiers: Generalized Quantifier Theory. [REVIEW]Edward Keenan - 2002 - Linguistics and Philosophy 25 (5-6):627-654.
  6.  4
    The Relative Contributions of Frontal and Parietal Cortex for Generalized Quantifier Comprehension.Christopher A. Olm, Corey T. McMillan, Nicola Spotorno, Robin Clark & Murray Grossman - 2014 - Frontiers in Human Neuroscience 8.
  7.  20
    A Generalized Quantifier Logic for Naked Infinitives.Jaap Does - 1991 - Linguistics and Philosophy 14 (3):241 - 294.
  8.  7
    A Generalized Quantifier Logic for Naked Infinitives.Jaap van der Does - 1991 - Linguistics and Philosophy 14 (3):241-294.
  9. Generalized Quantifier Theory and the Semantics of Focus.Sjaak De Mey - 1996 - In J. van der Does & Van J. Eijck (eds.), Quantifiers, Logic, and Language. Stanford University.
     
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  10.  7
    Fuhrken G.. Skolem-Type Normal Forms for First-Order Languages with a Generalized Quantifier. Fundamenta Mathematicae, Vol. 54 , Pp. 291–302.Vaught R. L.. The Completeness of Logic with the Added Quantifier “There Are Uncountably Many.” Fundamenta Mathematicae, Vol. 54 , Pp. 303–304. [REVIEW]Pawel Zbierski - 1968 - Journal of Symbolic Logic 33 (1):121-122.
  11. The Hierarchy Theorem for Generalized Quantifiers.Lauri Hella, Kerkko Luosto & Jouko Väänänen - 1996 - Journal of Symbolic Logic 61 (3):802-817.
    The concept of a generalized quantifier of a given similarity type was defined in [12]. Our main result says that on finite structures different similarity types give rise to different classes of generalized quantifiers. More exactly, for every similarity type t there is a generalized quantifier of type t which is not definable in the extension of first order logic by all generalized quantifiers of type smaller than t. This was proved for unary similarity (...)
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  12.  40
    On Vectorizations of Unary Generalized Quantifiers.Kerkko Luosto - 2012 - Archive for Mathematical Logic 51 (3-4):241-255.
    Vectorization of a class of structures is a natural notion in finite model theory. Roughly speaking, vectorizations allow tuples to be treated similarly to elements of structures. The importance of vectorizations is highlighted by the fact that if the complexity class PTIME corresponds to a logic with reasonable syntax, then it corresponds to a logic generated via vectorizations by a single generalized quantifier (Dawar in J Log Comput 5(2):213–226, 1995). It is somewhat surprising, then, that there have been (...)
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  13.  64
    Vector Space Semantics: A Model-Theoretic Analysis of Locative Prepositions. [REVIEW]Joost Zwarts & Yoad Winter - 2000 - Journal of Logic, Language and Information 9 (2):169-211.
    This paper introduces a compositional semantics of locativeprepositional phrases which is based on a vector space ontology.Model-theoretic properties of prepositions like monotonicity andconservativity are defined in this system in a straightforward way.These notions are shown to describe central inferences with spatialexpressions and to account for the grammaticality of prepositionmodification. Model-theoretic constraints on the set of possibleprepositions in natural language are specified, similar to the semanticuniversals of Generalized Quantifier Theory.
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  14.  62
    Monotonicity and Collective Quantification.Gilad Ben-avi & Yoad Winter - 2003 - Journal of Logic, Language and Information 12 (2):127-151.
    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 (...)
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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.  7
    Generalized Halfspaces in the Mixed-Integer Realm.Philip Scowcroft - 2009 - Notre Dame Journal of Formal Logic 50 (1):43-51.
    In the ordered Abelian group of reals with the integers as a distinguished subgroup, the projection of a finite intersection of generalized halfspaces is a finite intersection of generalized halfspaces. The result is uniform in the integer coefficients and moduli of the initial generalized halfspaces.
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  17.  56
    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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  18.  45
    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 (...)
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  19.  71
    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 (...)
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  20.  61
    One Connection Between Standard Invariance Conditions on Modal Formulas and Generalized Quantifiers.Dorit Ben Shalom - 2003 - 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 (...)
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  21.  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 (...)
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  22.  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 (...)
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  23.  97
    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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  24.  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 (...)
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  25.  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 (...)
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  26.  57
    The Elimination of Self-Reference: Generalized Yablo-Series and the Theory of Truth.P. Schlenker - 2007 - Journal of Philosophical Logic 36 (3):251-307.
    Although it was traditionally thought that self-reference is a crucial ingredient of semantic paradoxes, Yablo (1993, 2004) showed that this was not so by displaying an infinite series of sentences none of which is self-referential but which, taken together, are paradoxical. Yablo's paradox consists of a countable series of linearly ordered sentences s(0), s(1), s(2),... , where each s(i) says: For each k > i, s(k) is false (or equivalently: For no k > i is s(k) true). We generalize Yablo's (...)
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  27.  27
    'Only' Noun Phrases, Pseudo-Negative Generalized Quantifiers, Negative Polarity Items, and Monotonicity.J. Atlas - 1996 - Journal of Semantics 13 (4):265-328.
    The theory of Generalized Quantifiers has facilitated progress in the study of negation in natural language. In particular it has permitted the formulation of a DeMorgan taxonomy of logical strength of negative Noun Phrases (Zwarts 1996a,b). It has permitted the formulation of broad semantical generalizations to explain grammatical phenomena, e.g. the distribution of Negative Polarity Items (Ladusaw 1980; Linebarger 1981, 1987, 1991; Hoeksema 1986, 1995; Zwarts 1996a,b; Horn 1992, 1996b). In the midst of this theorizing Jaap Hoepelman invited me (...)
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  28.  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 (...)
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  29.  20
    Extensionality in Natural Language Quantification: The Case of Many and Few.Kristen A. Greer - 2014 - Linguistics and Philosophy 37 (4):315-351.
    This paper presents an extensional account of manyand few that explains data that have previously motivated intensional analyses of these quantifiers :599–620, 2000). The key insight is that their semantic arguments are themselves set intersections: the restrictor is the intersection of the predicates denoted by the N’ or the V’ and the restricted universe, U, and the scope is the intersection of the N’ and V’. Following Cohen, I assume that the universe consists of the union of alternatives to the (...)
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  30.  42
    Topic-Focus Articulation as Generalized Quantification.Jaroslav Peregrin - 1995 - In Peter Bosch & Rob van der Sandt (eds.), Focus and Natural Language Processing. Ibm Deutschland. pp. 49--57.
    Recent results of Partee, Rooth, Krifka and other formal semanticians confirm that topic-focus articulation (TFA) of sentence is relevant for its semantics. The essential import of TFA, which is more apparent in case of a language with relatively free word order such as Czech than in case of English, has been traditionally intensively studied by Czech linguists. In this paper we would like to indicate the possibility of the account for TFA in terms of the theory of generalized quantifiers, (...)
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  31.  5
    The Hierarchy Theorem for Generalized Quantifiers.Lauri Hella, Kerkko Luosto & Jouko Vaananen - 1996 - Journal of Symbolic Logic 61 (2):802-817.
    The concept of a generalized quantifier of a given similarity type was defined in [12]. Our main result says that on finite structures different similarity types give rise to different classes of generalized quantifiers. More exactly, for every similarity type $t$ there is a generalized quantifier of type $t$ which is not definable in the extension of first order logic by all generalized quantifiers of type smaller than $t$. This was proved for unary similarity (...)
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  32.  14
    The Hierarchy Theorem for Second Order Generalized Quantifiers.Juha Kontinen - 2006 - Journal of Symbolic Logic 71 (1):188 - 202.
    We study definability of second order generalized quantifiers on finite structures. Our main result says that for every second order type t there exists a second order generalized quantifier of type t which is not definable in the extension of second order logic by all second order generalized quantifiers of types lower than t.
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  33. A New Theory of Quantifiers and Term Connectives.Ken Akiba - 2009 - 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 boys (...)
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  34.  21
    On the Definability of the Quantifier “There Exist Uncountably Many”.Žarko Mijajlović - 1985 - Studia Logica 44 (3):257 - 264.
    In paper [5] it was shown that a great part of model theory of logic with the generalized quantifier Q x = there exist uncountably many x is reducible to the model theory of first order logic with an extra binary relation symbol. In this paper we consider when the quantifier Q x can be syntactically defined in a first order theory T. That problem was raised by Kosta Doen when he asked if the quantifier Q (...)
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  35.  25
    Definability and Quantifier Elimination for J3-Theories.Ítala M. L. D'Ottaviano - 1987 - Studia Logica 46 (1):37 - 54.
    The Joint Non-Trivialization Theorem, two Definability Theorems and the generalized Quantifier Elimination Theorem are proved for J 3-theories. These theories are three-valued with more than one distinguished truth-value, reflect certain aspects of model type logics and can. be paraconsistent. J 3-theories were introduced in the author's doctoral dissertation.
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  36.  9
    Generalized Quantifiers, Exception Phrases, and Logicality.S. Lappin - 1996 - Journal of Semantics 13 (3):197-220.
    On the Fregean view of NPs, quantified NPs are represented as operator-variable structures, while proper names are constants appearing in argument position. The Generalized Quantifier (GQ) approach characterizes quantified NPs as elements of a unified syntactic category and semantic type. According to the Logicality Thesis (May 1991), the distinction between quantified NPs, which undergo and operation of quantifier raising to yield operator-variable structures at Logical Form (LF), and non-quantified NPS, which appear in situ at LF, corresponds to (...)
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  37.  20
    An Application of Logic to Combinatorial Geometry: How Many Tetrahedra Are Equidecomposable with a Cube?Vladik Kreinovich & Olga Kosheleva - 1994 - Mathematical Logic Quarterly 40 (1):31-34.
    The main result of this paper were announced in Kosheleva — Kreinovich [7, 8]; for other algorithmic aspects of Hilbert's Third Problem see Kosheleva [6]. The authors are greatly thankful to Alexandr D. Alexandrov , Vladimir G. Boltianskii and Patrick Suppes for valuable discussions, and to the anonymous referee for important suggestions. This work was partially supported by an NSF grant No. CDA-9015006.
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  38.  4
    Generalized Quantifiers, Exception Phrases, and Logicality.Shalom Lappin - 1995 - Logic Journal of the IGPL 3 (2-3):203-222.
    On the Fregean view of NP's, quantified NP's are represented as operator-variable structures while proper names are constants appearing in argument position. The Generalized Quantifier approach characterizes quantified NP's and names as elements of a unified syntactic category and semantic type. According to the Logicality Thesis, the distinction between quantified NP's, which undergo an operation of quantifier raising to yield operator-variable structures at Logical Form and non-quantified NP's, which appear in situ at LF, corresponds to a difference (...)
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  39.  12
    Generalized Quantifiers and Pebble Games on Finite Structures.Phokion G. Kolaitis & Jouko A. Väänänen - 1995 - Annals of Pure and Applied Logic 74 (1):23-75.
    First-order logic is known to have a severely limited expressive power on finite structures. As a result, several different extensions have been investigated, including fragments of second-order logic, fixpoint logic, and the infinitary logic L∞ωω in which every formula has only a finite number of variables. In this paper, we study generalized quantifiers in the realm of finite structures and combine them with the infinitary logic L∞ωω to obtain the logics L∞ωω, where Q = {Qi: iε I} is a (...)
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  40. Generalized Logic: A Philosophical Perspective with Linguistic Applications.Gila Sher - 1989 - Dissertation, Columbia University
    The question motivating my investigation is: Are the basic philosophical principles underlying the "core" system of contemporary logic exhausted by the standard version? In particular, is the accepted narrow construal of the notion "logical term" justified? ;As a point of comparison I refer to systems of 1st-order logic with generalized quantifiers developed by mathematicians and linguists . Based on an analysis of the Tarskian conception of the role of logic I show that the standard division of terms into logical (...)
     
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  41.  30
    The Psychological Reality of Classical Quantifier Entailment Properties.G. Politzer - 2007 - Journal of Semantics 24 (4):331-343.
    A test of directional entailment properties of classical quantifiers defined by the theory of generalized quantifiers (Barwise & Cooper 1981) is described. Participants had to solve a task which consisted of four kinds of inference. In the first one, the premise was of the form ‘Q–hyponym–verb–blank predicate’, where Q is a classical quantifier (e.g. ‘Some cats are [ ]’), and the question was to indicate what, if anything, can be concluded by filling the slots in ‘...–hyperonym–verb–blank predicate’ (e.g. (...)
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  42.  72
    Number Sense and Quantifier Interpretation.Robin Clark & Murray Grossman - 2007 - Topoi 26 (1):51--62.
    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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  43.  26
    Improving Methodology of Quantifier Comprehension Experiments.Jakub Szymanik & Marcin Zajenkowski - 2009 - Neuropsychologia 47 (12):2682--2683.
    Szymanik (2007) suggested that the distinction between first-order and higher-order quantifiers does not coincide with the computational resources required to compute the meaning of quantifiers. Cognitive difficulty of quantifier processing might be better assessed on the basis of complexity of the minimal corresponding automata. For example, both logical and numerical quantifiers are first-order. However, computational devices recognizing logical quantifiers have a fixed number of states while the number of states in automata corresponding to numerical quantifiers grows with the rank (...)
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  44.  34
    The Downward Transfer of Elementary Satisfiability of Partition Logics.Y. Chen & E. Shen - 2000 - Mathematical Logic Quarterly 46 (4):477-488.
    We introduce a notion of pseudo-reachability in Gaifman graphs and suggest a graph-theoretic and uniform approach to the Löwenheim-Skolem-Tarski Theorems for partition logics as well as logics with general Malitz quantifiers.
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  45.  17
    Completeness and Interpolation of Almost‐Everywhere Quantification Over Finitely Additive Measures.João Rasga, Wafik Boulos Lotfallah & Cristina Sernadas - 2013 - Mathematical Logic Quarterly 59 (4-5):286-302.
  46.  39
    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 (...)
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  47. If-Clauses and Probability Operators.Paul Égré & Mikaël Cozic - 2011 - Topoi 30 (1):17-29.
    Adams’ thesis is generally agreed to be linguistically compelling for simple conditionals with factual antecedent and consequent. We propose a derivation of Adams’ thesis from the Lewis- Kratzer analysis of if-clauses as domain restrictors, applied to probability operators. We argue that Lewis’s triviality result may be seen as a result of inexpressibility of the kind familiar in generalized quantifier theory. Some implications of the Lewis- Kratzer analysis are presented concerning the assignment of probabilities to compounds of conditionals.
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  48.  27
    Quantifiers and Cognition: Logical and Computational Perspectives.Jakub Szymanik - 2016 - Springer.
    This volume on the semantic complexity of natural language explores the question why some sentences are more difficult than others. While doing so, it lays the groundwork for extending semantic theory with computational and cognitive aspects by combining linguistics and logic with computations and cognition. -/- Quantifier expressions occur whenever we describe the world and communicate about it. Generalized quantifier theory is therefore one of the basic tools of linguistics today, studying the possible meanings and the inferential (...)
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  49.  19
    Monotonicity Properties of Comparative Determiners.Hans Smessaert - 1996 - Linguistics and Philosophy 19 (3):295 - 336.
    This paper presents a generalization of the standard notions of left monotonicity (on the nominal argument of a determiner) and right monotonicity (on the VP argument of a determiner). Determiners such as “more than/at least as many as” or “fewer than/at most as many as”, which occur in so-called propositional comparison, are shown to be monotone with respect to two nominal arguments and two VP-arguments. In addition, it is argued that the standard Generalized Quantifier analysis of numerical determiners (...)
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  50.  16
    Vectorization Hierarchies of Some Graph Quantifiers.Lauri Hella & Juha Nurmonen - 2000 - 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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