Modal Logic and Invariance
Johan van Benthem, Denis Bonnay

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.