Bisimulations for Temporal Logic

We define bisimulations for temporal logic with Since and Until. This new notion is compared to existing notions of bisimulations, and then used to develop the basic model theory of temporal logic with Since and Until. Our results concern both invariance and definability. We conclude with a brief discussion of the wider applicability of our ideas.

[1]  Jan A. Bergstra,et al.  Logic of transition systems , 1994, J. Log. Lang. Inf..

[2]  Dov M. Gabbay,et al.  An Axiomitization of the Temporal Logic with Until and Since over the Real Numbers , 1990, J. Log. Comput..

[3]  M. de Rijke,et al.  A System of Dynamic Modal Logic , 1998, J. Philos. Log..

[4]  Rocco De Nicola,et al.  Three logics for branching bisimulation , 1995, JACM.

[5]  Ming Xu On some U,S-tense logics , 1988, J. Philos. Log..

[6]  Alessandro Berarducci,et al.  The interpretability logic of Peano arithmetic , 1990, Journal of Symbolic Logic.

[7]  Maarten de Rijke,et al.  Simulating Without Negation , 1997, J. Log. Comput..

[8]  Johan van Benthem,et al.  Back and Forth Between Modal Logic and Classical Logic , 1995, Log. J. IGPL.

[9]  John P. Burgess,et al.  Axioms for tense logic. I. "Since" and "until" , 1982, Notre Dame J. Formal Log..

[10]  Maarten de Rijke Modal model theory , 1995 .

[11]  Robin Milner,et al.  Algebraic laws for nondeterminism and concurrency , 1985, JACM.

[12]  Johan van Benthem,et al.  Language in action , 1991, J. Philos. Log..

[13]  M. Hollenberg Hennessy-Milner Classes and Process Algebra , 1994 .

[14]  M. de Rijke,et al.  A Lindström theorem for modal logic , 1994 .

[15]  Chen C. Chang,et al.  Model Theory: Third Edition (Dover Books On Mathematics) By C.C. Chang;H. Jerome Keisler;Mathematics , 1966 .

[16]  Jan van Eijck,et al.  Modal Logic, Transition Systems and Processes , 1993, J. Log. Comput..

[17]  Zohar Manna,et al.  The Temporal Logic of Reactive and Concurrent Systems , 1991, Springer New York.

[18]  Samuel B. Williams,et al.  ASSOCIATION FOR COMPUTING MACHINERY , 2000 .

[19]  Yde Venema,et al.  Expressiveness and Completeness of an Interval Tense Logic , 1990, Notre Dame J. Formal Log..

[20]  M. Hollenberg Bisimulation respecting first-order operations , 1996 .