Generalized quantifiers and modal logic
Copyright policy )Generalized quantifiers and modal logic
The paper studies several modal systems designed to represent generalized quantifiers. The main system QUANT has infinitely many modal operators \(M_ n\), which are interpreted in a set \(W\) under a valuation \(V\) as follows: \(M_ n\varphi\) is true at a point \(x\in W\) if the number of points in \(W\) at which \(\varphi\) is true under \(V\) is greater than \(n\) [cf. \textit{K. Fine}, Notre Dame J. Formal Logic 13, 516-520 (1972; Zbl 0242.02025)]. It is proved that every first-order definable quantifier is definable in the language of QUANT. Subsystems of QUANT and a system for representing higher order quantifiers as modal operators are also studied. Completeness, complexity, normal forms and some other standard problems are investigated for the systems under consideration.
- University of Amsterdam Netherlands
definability, Logic with extra quantifiers and operators, completeness, generalized quantifiers, Modal logic (including the logic of norms), modal logic
definability, Logic with extra quantifiers and operators, completeness, generalized quantifiers, Modal logic (including the logic of norms), modal logic
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