Modal logic and invariance

Journal of Applied Non-Classical Logics 18 (2-3):153-173 (2008)
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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 characterization of invariance and safety under bisimulation as natural conditions for logical operations in modal and dynamic logics, and some new transfer results between first-order logic and modal logic.



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Author Profiles

Denis Bonnay
Université Paris Nanterre
Johan Van Benthem
University of Amsterdam

References found in this work

Logicality and Invariance.Denis Bonnay - 2006 - Bulletin of Symbolic Logic 14 (1):29-68.
Logic, Logics, and Logicism.Solomon Feferman - 1999 - Notre Dame Journal of Formal Logic 40 (1):31-54.
Logical operations and invariance.Enrique Casanovas - 2007 - Journal of Philosophical Logic 36 (1):33 - 60.

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