Intuitionistic LTL and a New Characterization of Safety and Liveness

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.

[1]  Amir Pnueli,et al.  The Glory of the Past , 1985, Logic of Programs.

[2]  Jerzy Tiuryn,et al.  Logics of Programs , 1991, Handbook of Theoretical Computer Science, Volume B: Formal Models and Sematics.

[3]  A. Prasad Sistla,et al.  Safety, liveness and fairness in temporal logic , 1994, Formal Aspects of Computing.

[4]  Panagiotis Manolios,et al.  Safety and liveness in branching time , 2001, Proceedings 16th Annual IEEE Symposium on Logic in Computer Science.

[5]  Gordon D. Plotkin,et al.  A Framework for Intuitionistic Modal Logics , 1988, TARK.

[6]  Bowen Alpern,et al.  Defining Liveness , 1984, Inf. Process. Lett..

[7]  Bowen Alpern,et al.  Recognizing safety and liveness , 2005, Distributed Computing.

[8]  Dana Fisman,et al.  Reasoning with Temporal Logic on Truncated Paths , 2003, CAV.

[9]  Patrick Maier,et al.  A lattice-theoretic framework for circular assume-guarantee reasoning , 2003 .

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

[11]  J. Van Leeuwen,et al.  Handbook of theoretical computer science - Part A: Algorithms and complexity; Part B: Formal models and semantics , 1990 .

[12]  Martín Abadi,et al.  An Abstract Account of Composition , 1995, MFCS.

[13]  Martín Abadi,et al.  A Logical View of Composition , 1993, Theor. Comput. Sci..

[14]  Leslie Lamport,et al.  Proving the Correctness of Multiprocess Programs , 1977, IEEE Transactions on Software Engineering.

[15]  Martín Abadi,et al.  Conjoining specifications , 1995, TOPL.

[16]  Gordon Plotkin,et al.  A framework for intuitionistic modal logics: extended abstract , 1986 .

[17]  Bengt Jonsson,et al.  Assumption/Guarantee Specifications in Linear-Time Temporal Logic , 1996, Theor. Comput. Sci..

[18]  Amir Pnueli The Temporal Semantics of Concurrent Programs , 1981, Theor. Comput. Sci..

[19]  Rowan Davies,et al.  A temporal-logic approach to binding-time analysis , 1995, Proceedings 11th Annual IEEE Symposium on Logic in Computer Science.

[20]  Petr Hájek,et al.  Mathematical Foundations of Computer Science 1995 , 1995, Lecture Notes in Computer Science.

[21]  Panagiotis Manolios,et al.  A lattice-theoretic characterization of safety and liveness , 2003, PODC '03.

[22]  H. Peter Gumm Another Glance at the Alpern-Schneider Characterization of Safety and Liveness in Concurrent Executions , 1993, Inf. Process. Lett..