Axiomatizations of Interval Logics

Interval logic has been introduced as a temporal logic that provides higher-level constructs and an intuitive graphical representation, making it easier in interval logic than in other temporal logics to specify and reason about concurrency in software and hardware designs. In this paper we present axiomatizations for two propositional interval logics and relate these logics to Until Temporal Logic. All of these logics are discrete linear-time temporal logics with no next operator. The next operator obstructs the use of hierarchical abstraction and refinement, and makes reasoning about concurrency difficult.

[1]  Fred Kröger.  A Generalized Nexttime Operator in Temporal Logic , 1984, J. Comput. Syst. Sci..

[2]  G. Kutty,et al.  A graphic environment for temporal reasoning , 1995 .

[3]  Louise E. Moser,et al.  Graphical specifications for concurrent software systems , 1992, International Conference on Software Engineering.

[4]  Louise E. Moser,et al.  Completeness and Soundness of Axiomatizations for Temporal Logics. Without Next , 1994, Fundam. Informaticae.

[5]  Edmund M. Clarke,et al.  Reasoning about Networks with Many Identical Finite State Processes , 1989, Inf. Comput..

[6]  P. M. Melliar-Smith,et al.  An Interval-Based Temporal Logic , 1983, Logic of Programs.

[7]  Zohar Manna,et al.  A Hardware Semantics Based on Temporal Intervals , 1983, ICALP.

[8]  Leslie Lamport,et al.  What Good is Temporal Logic? , 1983, IFIP Congress.

[9]  Vaughan R. Pratt,et al.  Process logic: preliminary report , 1979, POPL.

[10]  Grzegorz Rozenberg,et al.  Linear Time, Branching Time and Partial Order in Logics and Models for Concurrency , 1988, Lecture Notes in Computer Science.

[11]  Yoav Shoham,et al.  A propositional modal logic of time intervals , 1991, JACM.

[12]  Rohit Parikh.  A decidability result for a second order process logic , 1978, 19th Annual Symposium on Foundations of Computer Science (sfcs 1978).

[13]  Amir Pnueli,et al.  A really abstract concurrent model and its temporal logic , 1986, POPL '86.

[14]  Louise E. Moser,et al.  An Automata-Theoretic Decision Procedure for Future Interval Logic , 1992, FSTTCS.

[15]  A. A. Aaby,et al.  Propositional Temporal Interval Logic is PSPACE Complete , 1988, CADE.

[16]  Amir Pnueli,et al.  A Choppy Logic , 1986, LICS.

[17]  David Harel,et al.  Process logic: Expressiveness, decidability, completeness , 1980, 21st Annual Symposium on Foundations of Computer Science (sfcs 1980).

[18]  David A. Plaisted,et al.  A Low Level Language for Obtaining Decision Procedure for Classes of temporal Logics , 1983, Logic of Programs.