Journal of Applied Non-Classical Logics 18 (2-3):153-173 (2008)
AbstractConsider 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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Citations of this work
Logical Constants, or How to use Invariance in Order to Complete the Explication of Logical Consequence.Denis Bonnay - 2014 - Philosophy Compass 9 (1):54-65.
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References found in this work
Computability and Logic.George Boolos, John Burgess, Richard P. & C. Jeffrey - 2002 - Cambridge University Press.
Modal Languages and Bounded Fragments of Predicate Logic.Hajnal Andréka, István Németi & Johan van Benthem - 1998 - Journal of Philosophical Logic 27 (3):217 - 274.
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.