Abstract
Classical linear-time temporal logic (LTL) is capable of specifying of and reasoning about infinite behaviors only. While this is appropriate for specifying non-terminating reactive systems, there are situations (e.g., assume-guarantee reasoning, run-time verification) when it is desirable to be able to reason about finite and infinite behaviors. We propose an interpretation of the operators of LTL on finite and infinite behaviors, which defines an intuitionistic temporal logic (ILTL). We compare the expressive power of LTL and ILTL. We demonstrate that ILTL is suitable for assume-guarantee reasoning and for expressing properties that relate finite and infinite behaviors. In particular, ILTL admits an elegant logical characterization of safety and liveness properties.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Abadi, M., Lamport, L.: Conjoining specifications. ACM Transactions on Programming Languages and Systems 17(3), 507–534 (1995)
Abadi, M., Merz, S.: An abstract account of composition. In: Hájek, P., Wiedermann, J. (eds.) MFCS 1995. LNCS, vol. 969, pp. 499–508. Springer, Heidelberg (1995)
Abadi, M., Plotkin, G.D.: A logical view of composition. Theoretical Computer Science 114, 3–30 (1993)
Alpern, B., Schneider, F.B.: Defining liveness. Information Processing Letters 21(4), 181–185 (1985)
Alpern, B., Schneider, F.B.: Recognizing safety and liveness. Distributed Computing 2(3), 117–126 (1987)
Davies, R.: A temporal-logic approach to binding-time analysis. In: Proceedings of the 11th IEEE Symposium on Logic in Computer Science (LICS), pp. 184–195. IEEE Computer Society Press, Los Alamitos (1996)
Eisner, C., Fisman, D., Havlicek, J., Lustig, Y., McIsaac, A., Van Campenhout, D.: Reasoning with temporal logic on truncated paths. In: Hunt Jr., W.A., Somenzi, F. (eds.) CAV 2003. LNCS, vol. 2725, pp. 27–39. Springer, Heidelberg (2003)
Allen Emerson, E.: Temporal and modal logic. In: van Leeuwen, J. (ed.) Handbook of Theoretical Computer Science, vol. B, pp. 995–1072. Elsevier, Amsterdam (1990)
Peter Gumm, H.: Another glance at the Alpern-Schneider characterization of safety and liveness in concurrent executions. Information Processing Letters 47(6), 291–294 (1993)
Jonsson, B., Tsay, Y.-K.: Assumption/guarantee specifications in lineartime temporal logic. Theoretical Computer Science 167, 47–72 (1996)
Lamport, L.: Proving the correctness of multiprocess programs. IEEE Transactions on Software Engineering 3(2), 125–143 (1977)
Lichtenstein, O., Pnueli, A., Zuck, L.: The glory of the past. In: Parikh, R. (ed.) Logic of Programs 1985. LNCS, vol. 193, pp. 196–218. Springer, Heidelberg (1985)
Maier, P.: A Lattice-Theoretic Framework For Circular Assume-Guarantee Reasoning. PhD thesis, Universität des Saarlandes, Saarbrücken (July 2003)
Maier, P.: Intuitionistic LTL and a new characterization of safety and liveness. Technical Report MPI-I-2004-2-002, Max-Planck-Institut für Informatik (2004)
Manolios, P., Trefler, R.: Safety and liveness in branching time. In: Proceedings of the 16th IEEE Symposium on Logic in Computer Science (LICS), pp. 366–374. IEEE Computer Society Press, Los Alamitos (2001)
Manolios, P., Trefler, R.: A lattice-theoretic characterization of safety and liveness. In: Proceedings of the 22nd ACM Symposium on Principles of Distributed Computing (PODC), pp. 325–333. ACM Press, New York (2003)
Plotkin, G., Stirling, C.: A framework for intuitionistic modal logics. In: Proceedings of the 1st Conference on Theoretical Aspects of Reasoning about Knowledge (TARK), pp. 399–406. Morgan Kaufmann, San Francisco (1986)
Pnueli, A.: The temporal semantics of concurrent programs. Theoretical Computer Science 13, 45–60 (1981)
Prasad Sistla, A.: Safety, liveness and fairness in temporal logic. Formal Aspects of Computing 6, 495–511 (1994)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Maier, P. (2004). Intuitionistic LTL and a New Characterization of Safety and Liveness. In: Marcinkowski, J., Tarlecki, A. (eds) Computer Science Logic. CSL 2004. Lecture Notes in Computer Science, vol 3210. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30124-0_24
Download citation
DOI: https://doi.org/10.1007/978-3-540-30124-0_24
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-23024-3
Online ISBN: 978-3-540-30124-0
eBook Packages: Springer Book Archive