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Directions in generalized quantifier theory

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Abstract

We give a condensed survey of recent research on generalized quantifiers in logic, linguistics and computer science, under the following headings: Logical definability and expressive power, Polyadic quantifiers and linguistic definability, Weak semantics and axiomatizability, Computational semantics, Quantifiers in dynamic settings, Quantifiers and modal logic, Proof theory of generalized quantifiers.

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Authors and Affiliations

  1. Institute for Logic, Language and Computation, University of Amsterdam, Plantage Muidergracht 24, 1018 TV, Amsterdam, The Netherlands

    Johan van Benthem

  2. Department of Philosophy, University of Stockholm, 106 91, Stockholm, Sweden

    Dag Westerståhl

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  1. Johan van Benthem
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Additional information

This paper was inspired by the symposium on Generalized Quantifiers held at the 5th European Summer School in Logic, Language and Information in Lisbon, August 1993. We feel that the work presented there motivates a survey of recent research areas and research problems in the field of generalized quantifiers. The speakers at the symposium, Natasha Alechina, Jaap van der Does, Lauri Hella, Michal Krynicki, Michiel van Lambalgen, Kerkko Luosto, Marcin Mostowski, and Jouko Väänänen, have cooperated and made (oral and/or written) contributions and comments to this research survey which we gratefully acknowledge, and without which it would not have been written. But it is easier to produce a paper with two authors than with ten, and so the present authors take full responsibility for the final formulation of the paper. In addition, we are grateful for comments received from some further colleagues, in particular, Dorit Ben-Shalom, Makoto Kanazawa, Victor Sanchez, Yde Venema and two anonymous referees.

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van Benthem, J., Westerståhl, D. Directions in generalized quantifier theory. Stud Logica 55, 389–419 (1995). https://doi.org/10.1007/BF01057805

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