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An axiomatization of full Computation Tree Logic

Published online by Cambridge University Press:  12 March 2014

M. Reynolds*
Affiliation:
School of Information Technology, Murdoch University, South Street, Perth, Western Australia 6150, E-mail: m.reynolds@murdoch.edu.au

Abstract

We give a sound and complete axiomatization for the full computation tree logic. CTL*, of R-generable models. This solves a long standing open problem in branching time temporal logic.

Type
Research Article
Copyright
Copyright © Association for Symbolic Logic 2001

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References

REFERENCES

[Bernholtz and Grumberg, 1994] Bernholtz, O. and Grumbero, O., Buy one, get one free!!!, Temporal logic, Proceedings of ICTL'94 (Gabbay, D. and Ohlbach, H., editors), LNAI, no. 827, Springer-Verlag, 1994, pp. 210224.CrossRefGoogle Scholar
[Burgess, 1980] Burgess, J. P., Decidability for branching time, Studia Logica, vol. 39 (1980), pp. 203218.CrossRefGoogle Scholar
[Clarke and Emerson, 1981] Clarke, E. and Emerson, E., Synthesis of synchronization skeletons for branching time temporal logic, Proc. IBM Workshop on Logic of Programs, Yorktown Heights, NY (Berlin), Springer, 1981, pp. 5271.Google Scholar
[Dam, 1992] Dam, M., R-generability, and definability in branching time logics, Information Processing Letters, vol. 41 (1992), pp. 281287.CrossRefGoogle Scholar
[Emerson, 1983] Emerson, E., Alternative semantics for temporal logics, Theoretical Computer Science, vol. 26 (1983).CrossRefGoogle Scholar
[Emerson, 1996] Emerson, E., Automated temporal reasoning for reactive systems, Logics for concurrency (Moller, F. and Birtwistle, G., editors), Springer Verlag, 1996, pp. 41101.CrossRefGoogle Scholar
[Emerson and Halpern, 1982] Emerson, E. and Halpern, J., Decision procedures and expressiveness in the temporal logic of branching time, Proc. 14th ACM Symp. on Theory of Computing, 1982.Google Scholar
[Emerson and Halpern, 1986] Emerson, E. and Halpern, J., ‘Sometimes’ and ‘not never’ revisited: on branching versus linear time, Journal of the ACM, vol. 33 (1986).CrossRefGoogle Scholar
[Emerson and Jutla, 1988] Emerson, E. and Jutla, C., Complexity of tree automata and modal logics of programs, 29th IEEE Foundations of Computer Science, Proceedings, IEEE, 1988.Google Scholar
[Emerson and Sistla, 1984] Emerson, E. and Sistla, A., Deciding full branching time logic, Information and Control, vol. 61 (1984), pp. 175201.CrossRefGoogle Scholar
[Emerson, 1990] Emerson, E. A., Temporal and modal logic, Handbook of theoretical computer science (van Leeuwen, J., editor), vol. B, Elsevier, Amsterdam, 1990.Google Scholar
[Gabbay, Hodkinson, and Reynolds, 1994] Gabbay, D., Hodkinson, I., and Reynolds, M., Temporal logic: Mathematical foundations and computational aspects, vol. 1, Oxford University Press, 1994.Google Scholar
[Gabbay, 1981] Gabbay, D. M., An irreflexivity lemma with applications to axiomatizations of conditions on tense frames, Aspects of philosophical logic (Monnich, U., editor), Reidel, Dordrecht, 1981, pp. 6789.CrossRefGoogle Scholar
[Gabbay, Pnueli, Shelah, and Stavi, 1980] Gabbay, D. M., Pnueli, A., Shelah, S., and Stavi, J., On the temporal analysis offairness, 7th ACM Symposium on Principles of Programming Languages, Las Vegas, 1980, pp. 163173.Google Scholar
[Kaivola, 1996] Kaivola, R., Axiomatising extended computation tree logic, in trees in algebra a programming, CAAP'96, 21st International Colloquium, Proceedings, vol. 1059, Springer, 1996, pp. 87101.Google Scholar
[Kesten and Pnueli, 1995] Kesten, Yonit and Pnueli, Amir, A complete proof systems for QPTL, Proceedings, Tenth Annual IEEE Symposium on Logic in Computer Science (San Diego, California), IEEE Computer Society Press, 26-29 06 1995, pp. 212.CrossRefGoogle Scholar
[McNaughton, 1966] McNaughton, R., Testing and generating infinite sequences by finite automata, Information and Control, vol. 9 (1966), pp. 521530.CrossRefGoogle Scholar
[Pnueli, 1977] Pnueli, A., The temporal logic of programs, Proceedings of the Eighteenth Symposium on Foundations of Computer Science (Providence, RI), 1977, pp. 4657.Google Scholar
[Safra, 1988] Safra, S., On the complexity of ω-automata, Proceedings of 29th IEEE Symposium on the Foundations of Computer Science, 1988.Google Scholar
[Stirling, 1992] Stirling, C., Modal and temporal logics, Handbook of Logic in Computer Science, Volume 2 (Abramsky, S., Gabbay, D., and Maibaum, T., editors), OUP, 1992, pp. 477563.CrossRefGoogle Scholar
[Thomason, 1984] Thomason, R., Combinations of tense and modality, Handbook of philosophical logic, Vol II: Extensions of classical logic (Gabbay, D. and Guenthner, F., editors), Reidel, Dordrecht, 1984, pp. 135165.CrossRefGoogle Scholar
[Vardi and Stockmeyer, 1985] Vardi, M. and Stockmeyer, L., Improved upper and lower bounds for modal logics of programs, 17th ACM Symp. on Theory of Computing, Proceedings, ACM, 1985, pp. 240251.Google Scholar
[Walukiewicz, 1995] Walukiewicz, I., A complete deductive system for the μ-calculus, BRICS Research Report RS-95-6, Department of Computer Science, University of Aarhus, Denmark, 1995.Google Scholar
[Zanardo, 1985] Zanardo, A., A finite axiomatization of the set of strongly valid Ockamist formulas, Journal of Philosophical Logic, vol. 14 (1985), pp. 447468.CrossRefGoogle Scholar
[Zanardo, 1996] Zanardo, A., Branching-time logic with quantification over branches: the point of view of modal logic, this Journal, vol. 61 (1996), pp. 139.Google Scholar
[Zanardo, Barcellan, and Reynolds, 1999] Zanardo, A., Barcellan, B., and Reynolds, M., Non-definability of the class of complete bundled trees, Logic Journal of the IGPL, vol. 7 (1999), no. 1, pp. 125136.CrossRefGoogle Scholar
[Zanardo and Carmo, 1993] Zanardo, Alberto and Carmo, José, Ockhamist computational logic: Past-sensitive necessitation in CTL, Journal of Logic and Computation, vol. 3 (1993), no. 3, pp. 249268.CrossRefGoogle Scholar