Results for 'generalized quantifiers'

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  1. Jon Barwise.Noun Phrases & Generalized Quantifiers - 1987 - In Peter Gärdenfors (ed.), Generalized Quantifiers. Reidel Publishing Company. pp. 31--1.
     
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  2. Dag Westerstahl.Branching Generalized Quantifiers - 1987 - In Peter Gärdenfors (ed.), Generalized Quantifiers. Reidel Publishing Company. pp. 269.
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  3. 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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  4.  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 (...)
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  5.  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 (...)
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  6.  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 (...)
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  7.  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 (...)
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  8.  58
    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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  9.  67
    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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  10.  73
    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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  11.  54
    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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  12.  14
    Relativized Logspace and Generalized Quantifiers Over Finite Ordered Structures.Georg Gottlob - 1997 - Journal of Symbolic Logic 62 (2):545-574.
    We here examine the expressive power of first order logic with generalized quantifiers over finite ordered structures. In particular, we address the following problem: Given a family Q of generalized quantifiers expressing a complexity class C, what is the expressive power of first order logic FO(Q) extended by the quantifiers in Q? From previously studied examples, one would expect that FO(Q) captures L C , i.e., logarithmic space relativized to an oracle in C. We show (...)
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  13.  12
    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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  14.  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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  15.  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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  16. 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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  17.  40
    First order predicate logic with generalized quantifiers.Per Lindström - 1966 - Theoria 32 (3):186--195.
  18. Dynamic Generalized Quantifiers.Martin van den Berg - 1996 - In J. van der Does & Van J. Eijck (eds.), Quantifiers, Logic, and Language. Stanford University. pp. 63--94.
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  19. Neural Basis for Generalized Quantifiers Comprehension.C. T. Mcmillan, R. Clark, P. Moore, C. Devita & M. Grossman - 2005 - Neuropsychologia 43:1729--1737.
  20. Generalized Quantifiers and Computation, 9th European Summer School in Logic, Language, and Information, ESSLLI'97 Workshop, Aix-En-Provence, France, August 11-22, 1997, Revised Lectures.Jouko Vaananen - 1997 - Springer.
  21. 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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  22.  24
    On Second-Order Generalized Quantifiers and Finite Structures.Anders Andersson - 2002 - Annals of Pure and Applied Logic 115 (1--3):1--32.
    We consider the expressive power of second - order generalized quantifiers on finite structures, especially with respect to the types of the quantifiers. We show that on finite structures with at most binary relations, there are very powerful second - order generalized quantifiers, even of the simplest possible type. More precisely, if a logic is countable and satisfies some weak closure conditions, then there is a generalized second - order quantifier which is monadic, unary (...)
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  23.  14
    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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  24.  6
    Convergence Laws for Very Sparse Random Structures with Generalized Quantifiers.Risto Kaila - 2002 - Mathematical Logic Quarterly 48 (2):301-320.
    We prove convergence laws for logics of the form equation image, where equation image is a properly chosen collection of generalized quantifiers, on very sparse finite random structures. We also study probabilistic collapsing of the logics equation image, where equation image is a collection of generalized quantifiers and k ∈ ℕ+, under arbitrary probability measures of finite structures.
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  25. Generalized Quantifiers and Natural Language.John Barwise & Robin Cooper - 1981 - Linguistics and Philosophy 4 (2):159--219.
  26.  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 (...)
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  27.  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 few (...)
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  28.  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 (...)
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  29.  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⋯ (...)
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  30.  75
    Conservative Generalized Quantifiers and Presupposition.Tim Fernando - manuscript
    Conservativity in generalized quantifiers is linked to presupposition filtering, under a propositions-as-types analysis extended with dependent quantifiers. That analysis is underpinned by modeltheoretically interpretable proofs which inhabit propositions they prove, thereby providing objects for quantification and hooks for anaphora.
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  31.  56
    Partially-Ordered (Branching) Generalized Quantifiers: A General Definition.Gila Sher - 1997 - Journal of Philosophical Logic 26 (1):1-43.
    Following Henkin's discovery of partially-ordered (branching) quantification (POQ) with standard quantifiers in 1959, philosophers of language have attempted to extend his definition to POQ with generalized quantifiers. In this paper I propose a general definition of POQ with 1-place generalized quantifiers of the simplest kind: namely, predicative, or "cardinality" quantifiers, e.g., "most", "few", "finitely many", "exactly α", where α is any cardinal, etc. The definition is obtained in a series of generalizations, extending the original, (...)
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  32.  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 (...)
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  33.  56
    Aristotelian Syllogisms and Generalized Quantifiers.Dag Westerståhl - 1989 - Studia Logica 48 (4):577-585.
    The paper elaborates two points: i) There is no principal opposition between predicate logic and adherence to subject-predicate form, ii) Aristotle's treatment of quantifiers fits well into a modern study of generalized quantifiers.
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  34.  9
    Branching Generalized Quantifiers and Natural Language.Dag Westerståhl - 1987 - In Peter Gärdenfors (ed.), Generalized Quantifiers. Reidel Publishing Company. pp. 269--298.
  35.  33
    Generalized Quantifiers and Number Sense.Robin Clark - 2011 - Philosophy Compass 6 (9):611-621.
    Generalized quantifiers are functions from pairs of properties to truth-values; these functions can be used to interpret natural language quantifiers. The space of such functions is vast and a great deal of research has sought to find natural constraints on the functions that interpret determiners and create quantifiers. These constraints have demonstrated that quantifiers rest on number and number sense. In the first part of the paper, we turn to developing this argument. In the remainder, (...)
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  36.  5
    Partially-Ordered Generalized Quantifiers: A General Definition.G. Y. Sher - 1997 - Journal of Philosophical Logic 26 (1):1-43.
    Following Henkin's discovery of partially-ordered quantification with standard quantifiers in 1959, philosophers of language have attempted to extend his definition to POQ with generalized quantifiers. In this paper I propose a general definition of POQ with 1-place generalized quantifiers of the simplest kind: namely, predicative, or "cardinality" quantifiers, e.g., "most", "few", "finitely many", "exactly α", where α is any cardinal, etc. The definition is obtained in a series of generalizations, extending the original, Henkin definition (...)
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  37.  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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  38.  2
    There-Sentences and Generalized Quantifiers.Lars G. Johnsen - 1987 - In Peter Gärdenfors (ed.), Generalized Quantifiers. Reidel Publishing Company. pp. 93--107.
  39.  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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  40.  10
    Preliminaries to the Treatment of Generalized Quantifiers in Situation Semantics.Robin Cooper - 1987 - In Peter Gärdenfors (ed.), Generalized Quantifiers. Reidel Publishing Company. pp. 73--91.
  41.  10
    Generalized Quantifiers in Natural Language.Johan Van Benthem & Alice Ter Meulen (eds.) - 1984 - Foris Publications.
    REFERENCES Barwise, J. & R. Cooper (1981) — 'Generalized Quantifiers and Natural Language', Linguistics and Philosophy 4:2159-219. Van Benthem, J. (1983a) — ' Five Easy Pieces', in Ter Meulen (ed.), 1-17. Van Benthem, J. (1983b) ...
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  42.  19
    A Representation Theorem for Languages with Generalized Quantifiers Through Back-and-Forth Methods.Renato H. L. Pedrosa & Antonio M. A. Sette - 1988 - Studia Logica 47 (4):401 - 411.
    We obtain in this paper a representation of the formulae of extensions ofL by generalized quantifiers through functors between categories of first-order structures and partial isomorphisms. The main tool in the proofs is the back-and-forth technique. As a corollary we obtain the Caicedo's version of Fraïssés theorem characterizing elementary equivalence for such languages. We also discuss informally some geometrical interpretations of our results.
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  43. Generalized Quantifiers and Plurals1.Peter Gdrdenfors - 1987 - In Peter Gärdenfors (ed.), Generalized Quantifiers. Reidel Publishing Company. pp. 31--151.
     
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  44. Generalized Quantifiers: Finite Versus Infinite.Kees van Deemter - 1984 - In Johan Van Benthem & Alice Ter Meulen (eds.), Generalized Quantifiers in Natural Language. Foris Publications.
     
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  45.  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 a difference (...)
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  46.  6
    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 in logicality (...)
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  47.  9
    Generalized Quantifiers and Natural Language.Jon Barwise - 1980 - Linguistics and Philosophy 4:159.
  48.  45
    Decomposing Generalized Quantifiers.Dag Westerståhl - 2008 - Review of Symbolic Logic 1 (3):355-371.
    This note explains the circumstances under which a type 1 quantifier can be decomposed into a type 1, 1 quantifier and a set, by fixing the first argument of the former to the latter. The motivation comes from the semantics of Noun Phrases (also called Determiner Phrases) in natural languages, but in this article, I focus on the logical facts. However, my examples are taken among quantifiers appearing in natural languages, and at the end, I sketch two more principled (...)
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  49. Natural Deduction for Generalized Quantifiers.van M. Lambalgen - 1996 - In J. van der Does & Van J. Eijck (eds.), Quantifiers, Logic, and Language. Stanford University. pp. 54--225.
     
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  50.  90
    Hierarchies of Monadic Generalized Quantifiers.Kerkko Luosto - 2000 - Journal of Symbolic Logic 65 (3):1241-1263.
    A combinatorial criterium is given when a monadic quantifier is expressible by means of universe-independent monadic quantifiers of width n. It is proved that the corresponding hierarchy does not collapse. As an application, it is shown that the second resumption (or vectorization) of the Hartig quantifier is not definable by monadic quantifiers. The techniques rely on Ramsey theory.
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