Generalized quantifiers and modal logic

Journal of Logic, Language and Information 2 (1):19-58 (1993)
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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.



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Wiebe Van Der Hoek
University of Liverpool

Citations of this work

Arithmetizations of Syllogistic à la Leibniz.Vladimir Sotirov - 1999 - Journal of Applied Non-Classical Logics 9 (2-3):387-405.
A note on graded modal logic.Maarten de Rijke - 2000 - Studia Logica 64 (2):271-283.
Guards, Bounds, and generalized semantics.Johan van Benthem - 2005 - Journal of Logic, Language and Information 14 (3):263-279.

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References found in this work

Questions about quantifiers.Johan van Benthem - 1984 - Journal of Symbolic Logic 49 (2):443-466.
The modal logic of inequality.Maarten de Rijke - 1992 - Journal of Symbolic Logic 57 (2):566-584.
Solvable cases of the decision problem.Wilhelm Ackermann - 1954 - Amsterdam,: North-Holland Pub. Co..
Qualitative probability as an intensional logic.Peter Gärdenfors - 1975 - Journal of Philosophical Logic 4 (2):171 - 185.
In so many possible worlds.Kit Fine - 1972 - Notre Dame Journal of Formal Logic 13 (4):516-520.

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