Generalized quantifiers and modal logic

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
Maarten de Rijke (1992). The Modal Logic of Inequality. Journal of Symbolic Logic 57 (2):566-584.
Johan van Benthem (1984). Questions About Quantifiers. Journal of Symbolic Logic 49 (2):443-466.
Kit Fine (1972). In so Many Possible Worlds. Notre Dame Journal of Formal Logic 13 (4):516-520.

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

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