Generalized quantifiers and modal logic

Abstract
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 modal systems and of systems in the quantifier tradition, complexity as well as syntactic characterizations of special semantic constraints. Throughout the paper several techniques current in the theory of generalized quantifiers are used to obtain results in modal logic, and conversely.
Keywords Modal logic  generalized quantifiers  axiomatic completeness  complexity  definability
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DOI 10.1007/BF01051767
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References found in this work BETA
The Modal Logic of Inequality.Maarten de Rijke - 1992 - Journal of Symbolic Logic 57 (2):566-584.
Questions About Quantifiers.van Benthem Johan - 1984 - Journal of Symbolic Logic 49 (2):443-466.
In so Many Possible Worlds.Kit Fine - 1972 - Notre Dame Journal of Formal Logic 13 (4):516-520.
On the Semantics of Graded Modalities.Wiebe Van der Hoek - 1992 - Journal of Applied Non-Classical Logics 2 (1):81-123.
Solvable Cases of the Decision Problem.W. Ackermann - 1954 - Amsterdam: North-Holland Pub. Co..

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Citations of this work BETA
Guards, Bounds, and Generalized Semantics.Johan van Benthem - 2005 - Journal of Logic, Language and Information 14 (3):263-279.
Toward Model-Theoretic Modal Logics.Minghui Ma - 2010 - Frontiers of Philosophy in China 5 (2):294-311.

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