A Van Benthem/Rosen theorem for coalgebraic predicate logic

A Van Benthem/Rosen theorem for coalgebraic predicate logic AbstractCoalgebraic modal logic serves as a unifying framework to study a wide range of modal logics beyond the relational realm, including probabilistic and graded logics as well as conditional logics and logics based on neighbourhoods and games. Coalgebraic predicate logic (CPL), a generalization of a neighbourhood-based first-order logic introduced by Chang, has been identified as a natural first-order extension of coalgebraic modal logic, which in particular coincides with the standard first-order correspondence language when instantiated to Kripke-style relational modal operators. Here, we generalize to the CPL setting the classical van Benthem/Rosen theorem stating that both over arbitrary and over finite models, modal logic is precisely the bisimulation-invariant fragment of first-order logic. As instances of this generic result, we obtain corresponding characterizations for, e.g. conditional logic, neighbourhood logic (i.e. classical modal logic) and monotone modal logic. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Logic and Computation Oxford University Press

A Van Benthem/Rosen theorem for coalgebraic predicate logic

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Publisher
Oxford University Press
Copyright
© The Author, 2015. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oup.com
ISSN
0955-792X
eISSN
1465-363X
D.O.I.
10.1093/logcom/exv043
Publisher site
See Article on Publisher Site

Abstract

AbstractCoalgebraic modal logic serves as a unifying framework to study a wide range of modal logics beyond the relational realm, including probabilistic and graded logics as well as conditional logics and logics based on neighbourhoods and games. Coalgebraic predicate logic (CPL), a generalization of a neighbourhood-based first-order logic introduced by Chang, has been identified as a natural first-order extension of coalgebraic modal logic, which in particular coincides with the standard first-order correspondence language when instantiated to Kripke-style relational modal operators. Here, we generalize to the CPL setting the classical van Benthem/Rosen theorem stating that both over arbitrary and over finite models, modal logic is precisely the bisimulation-invariant fragment of first-order logic. As instances of this generic result, we obtain corresponding characterizations for, e.g. conditional logic, neighbourhood logic (i.e. classical modal logic) and monotone modal logic.

Journal

Journal of Logic and ComputationOxford University Press

Published: Apr 1, 2017

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