Model Checking for Combined Logics with an Application to Mobile Systems

In this paper, we develop model checking procedures for three ways of combining (temporal) logics: temporalization, independent combination, and join. We prove that they are terminating, sound, and complete, we analyze their computational complexity, and we report on experiments with implementations. We take a close look at mobile systems and show how the proposed combined model checking framework can be successfully applied to the specification and verification of their properties.

[1]  Marcus Kracht,et al.  Properties of independently axiomatizable bimodal logics , 1991, Journal of Symbolic Logic.

[2]  D. Gabbay,et al.  Many-Dimensional Modal Logics: Theory and Applications , 2003 .

[3]  Witold Charatonik,et al.  The Decidability of Model Checking Mobile Ambients , 2001, CSL.

[4]  Edmund M. Clarke Automatic Verification of Finite-state Concurrent Systems , 1994, Application and Theory of Petri Nets.

[5]  Leslie Lamport,et al.  Specifying Concurrent Program Modules , 1983, TOPL.

[6]  Dov M. Gabbay,et al.  Adding a temporal dimension to a logic system , 1992, J. Log. Lang. Inf..

[7]  Frank Wolter The product of converse PDL and polymodal K , 2000, J. Log. Comput..

[8]  Luca Cardelli,et al.  Anytime, anywhere: modal logics for mobile ambients , 2000, POPL '00.

[9]  Franz Baader,et al.  A Multi-Dimensional Terminological Knowledge Representation Language , 1993, IJCAI.

[10]  Maarten Marx,et al.  A Road-Map on Complexity for Hybrid Logics , 1999, CSL.

[11]  Ágnes Kurucz S5 x S5 x S5 Lacks the Finite Model Property. , 2000 .

[12]  Ronald Fagin,et al.  Reasoning about knowledge , 1995 .

[13]  Marcelo Finger Handling database updates in two-dimensional temporal logic , 1992, J. Appl. Non Class. Logics.

[14]  M. de Rijke,et al.  Hybrid logics on linear structures: expressivity and complexity , 2003, 10th International Symposium on Temporal Representation and Reasoning, 2003 and Fourth International Conference on Temporal Logic. Proceedings..

[15]  W. van der Hoek,et al.  Epistemic logic for AI and computer science , 1995, Cambridge tracts in theoretical computer science.

[16]  Dov M. Gabbay,et al.  Combining Temporal Logic Systems , 1996, Notre Dame J. Formal Log..

[17]  Maarten Marx,et al.  The Computational Complexity of Hybrid Temporal Logics , 2000, Log. J. IGPL.

[18]  Frank Wolter,et al.  Fusions of Modal Logics Revisited , 1996, Advances in Modal Logic.

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

[20]  Patrick Blackburn,et al.  Representation, Reasoning, and Relational Structures: a Hybrid Logic Manifesto , 2000, Log. J. IGPL.

[21]  Joseph Y. Halpern,et al.  Model Checking vs. Theorem Proving: A Manifesto , 1991, KR.

[22]  Fred Kröger,et al.  Temporal Logic of Programs , 1987, EATCS Monographs on Theoretical Computer Science.

[23]  Dov M. Gabbay,et al.  Products of Modal Logics, Part 1 , 1998, Log. J. IGPL.

[24]  Orna Kupferman,et al.  An automata-theoretic approach to modular model checking , 2000, TOPL.

[25]  Stephan Merz,et al.  Model Checking , 2000 .

[26]  Frank Wolter,et al.  The finite model property in tense logic , 1995, Journal of Symbolic Logic.

[27]  Orna Kupferman,et al.  Modular Model Checking , 1997, COMPOS.

[28]  E. Allen Emerson,et al.  Temporal and Modal Logic , 1991, Handbook of Theoretical Computer Science, Volume B: Formal Models and Sematics.

[29]  Marcelo Finger,et al.  Two-dimensional Executable Temporal Logic for Bitemporal Databases , 2000 .

[30]  Joseph Y. Halpern,et al.  The Complexity of Reasoning about Knowledge and Time. I. Lower Bounds , 1989, J. Comput. Syst. Sci..

[31]  Cristina Sernadas,et al.  Synchronization of Logics with Mixed Rules: Completeness Preservation , 1997, AMAST.

[32]  Frank Wolter,et al.  Satis ability problem in description logics with modal operators , 1998 .

[33]  Edith Hemaspaandra Complexity transfer for modal logic , 1994, Proceedings Ninth Annual IEEE Symposium on Logic in Computer Science.

[34]  Maarten Marx,et al.  Complexity of Products of Modal Logics , 1999, J. Log. Comput..

[35]  Frank Wolter,et al.  Completeness and decidability of tense logics closely related to logics above K4 , 1997, Journal of Symbolic Logic.

[36]  Joeri Engelfriet,et al.  Minimal Temporal Epistemic Logic , 1996, Notre Dame J. Formal Log..

[37]  Cliff B. Jones,et al.  Specification and Design of (Parallel) Programs , 1983, IFIP Congress.

[38]  Witold Charatonik,et al.  The Complexity of Model Checking Mobile Ambients , 2001, FoSSaCS.

[39]  Maarten Marx,et al.  Hybrid logics: characterization, interpolation and complexity , 2001, Journal of Symbolic Logic.

[40]  M. de Rijke,et al.  Model Checking for combined logics , 2000 .

[41]  Jan Vitek,et al.  Secure Internet Programming: Security Issues for Mobile and Distributed Objects , 1999 .

[42]  Joseph A. Goguen,et al.  Institutions: abstract model theory for specification and programming , 1992, JACM.

[43]  M. de Rijke,et al.  Model checking hybrid logics , 2003 .

[44]  Luca Cardelli,et al.  Mobile Ambients , 1998, FoSSaCS.

[45]  Frank Wolter,et al.  A Counterexample in Tense Logic , 1996, Notre Dame J. Formal Log..