PP-2008-30: Modal Logic and Invariance

PP-2008-30: van Benthem, Johan and Bonnay, Denis (2008) Modal Logic and Invariance. [Report]

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Abstract

Consider any logical system, what is its natural repertoire of logical operations? This question has been raised in particular for first-order logic and its extensions with generalized quantifiers, and various characterizations in terms of semantic invariance have been proposed. In this paper, our main concern is with modal and dynamic logics. Drawing on previous work on invariance for first-order operations, we find an abstract connection between the kind of logical operations a system uses and the kind of invariance conditions the system respects. This analysis yields (a) a characterization of invariance and safety under bisimulation as natural conditions for logical operations in modal and dynamic logics, and (b) some new transfer results between first-order logic and modal logic.

Item Type: Report
Report Nr: PP-2008-30
Series Name: Prepublication (PP) Series
Year: 2008
Uncontrolled Keywords: modal logic; dynamic logic; bisimulation; ; potential isomorphism; first-order logic; ; invariance; logical constants.
Subjects: Logic
Depositing User: Johan Benthem
Date Deposited: 12 Oct 2016 14:37
Last Modified: 12 Oct 2016 14:37
URI: https://eprints.illc.uva.nl/id/eprint/304

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