Clausal temporal resolution

In this article, we examine how clausal resolution can be applied to a specific, but widely used, nonclassical logic, namely discrete linear temporal logic. Thus, we first define a normal form for temporal formulae and show how arbitrary temporal formulae can be translated into the normal form, while preserving satisfiability. We then introduce novel resolution rules that can be applied to formulae in this normal form, provide a range of examples, and examine the correctness and complexity of this approach. Finally, we describe related work and future developments concerning this work.

[1]  Martín Abadi,et al.  Temporal-logic theorem proving , 1987 .

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

[3]  Gerard J. Holzmann,et al.  The Model Checker SPIN , 1997, IEEE Trans. Software Eng..

[4]  John P. Burgess,et al.  The decision problem for linear temporal logic , 1985, Notre Dame J. Formal Log..

[5]  Amir Pnueli,et al.  On the Development of Reactive Systems , 1989, Logics and Models of Concurrent Systems.

[6]  Enrico Franconi,et al.  Introducing temporal description logics , 1999, Proceedings. Sixth International Workshop on Temporal Representation and Reasoning. TIME-99.

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

[8]  Clare Dixon,et al.  Search Strategies for Resolution in Temporal Logics , 1996, CADE.

[9]  Michael Fisher,et al.  A Normal Form for First-Order Temporal Formulae , 1992, CADE.

[10]  Zohar Manna,et al.  Temporal Verification of Reactive Systems , 1995, Springer New York.

[11]  J. A. Robinson,et al.  A Machine-Oriented Logic Based on the Resolution Principle , 1965, JACM.

[12]  A. Prasad Sistla,et al.  The complexity of propositional linear temporal logics , 1982, STOC '82.

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

[14]  Richard C. T. Lee,et al.  Symbolic logic and mechanical theorem proving , 1973, Computer science classics.

[15]  Clare Dixon,et al.  Using Otter for Temporal Resolution , 2000 .

[16]  Jai Srinivasan,et al.  Branching time temporal logic , 1988, REX Workshop.

[17]  Larry Wos,et al.  Automated Reasoning: Introduction and Applications , 1984 .

[18]  G. Venkatesh,et al.  A Decision Method for Temporal Logic Based on Resolution , 1985, FSTTCS.

[19]  Pierre Wolper,et al.  The Complementation Problem for Büchi Automata with Appplications to Temporal Logic , 1987, Theor. Comput. Sci..

[20]  D. Loveland.  A Linear Format for Resolution , 1970 .

[21]  D. Luckham.  Refinement Theorems in Resolution Theory , 1970 .

[22]  Clare Dixon,et al.  The Set of Support strategy in temporal resolution , 1998, Proceedings. Fifth International Workshop on Temporal Representation and Reasoning (Cat. No.98EX157).

[23]  Clare Dixon,et al.  Parallel Temporal Resolution , 1995 .

[24]  David A. Plaisted,et al.  A Structure-Preserving Clause Form Translation , 1986, J. Symb. Comput..

[25]  Colin Stirling,et al.  Modal and temporal logics , 1993, LICS 1993.

[26]  Michael Fisher,et al.  A Resolution Method for Temporal Logic , 1991, IJCAI.

[27]  J. A. Robinson,et al.  Automatic Deduction with Hyper-Resolution , 1983 .

[28]  Larry Wos,et al.  Efficiency and Completeness of the Set of Support Strategy in Theorem Proving , 1965, JACM.

[29]  L. Wos,et al.  The unit preference strategy in theorem proving , 1899, AFIPS '64 (Fall, part I).

[30]  Pierre Wolper.  Temporal Logic Can Be More Expressive , 1983, Inf. Control..

[31]  Michael Fisher,et al.  A resolution method for CTL branching-time temporal logic , 1997, Proceedings of TIME '97: 4th International Workshop on Temporal Representation and Reasoning.

[32]  Dov M. Gabbay,et al.  The Declarative Past and Imperative Future: Executable Temporal Logic for Interactive Systems , 1987, Temporal Logic in Specification.

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

[34]  Chin-Liang Chang.  The Unit Proof and the Input Proof in Theorem Proving , 1970, JACM.

[35]  Clare Dixon,et al.  Guiding Clausal Temporal Resolution , 2000 .

[36]  Michael Fisher,et al.  Transformation and Synthesis in METATEM Part I: Propositional METATEM , 1992 .

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

[38]  William McCune,et al.  OTTER 3.0 Reference Manual and Guide , 1994 .

[39]  Larry Wos,et al.  Automated reasoning (2nd ed.): introduction and applications , 1992 .

[40]  Dov M. Gabbay,et al.  The imperative future: principles of executable temporal logic , 1996 .

[41]  Zohar Manna,et al.  Temporal verification of reactive systems - safety , 1995 .

[42]  Michael Fisher,et al.  A Normal Form for Temporal Logics and its Applications in Theorem-Proving and Execution , 1997, J. Log. Comput..

[43]  Ana R. Cavalli,et al.  A Decision Method for Linear Temporal Logic , 1984, CADE.

[44]  Ian Horrocks.  The FaCT System , 1998, TABLEAUX.

[45]  Saharon Shelah,et al.  On the temporal analysis of fairness , 1980, POPL '80.

[46]  Martín Abadi,et al.  Nonclausal Temporal Deduction , 1985, Logic of Programs.

[47]  Sushil Jajodia,et al.  Temporal Databases: Theory, Design, and Implementation , 1993 .

[48]  Ullrich Hustadt,et al.  An empirical analysis of modal theorem provers , 1999, J. Appl. Non Class. Logics.

[49]  Martín Abadi,et al.  Nonclausal deduction in first-order temporal logic , 1990, JACM.

[50]  David I. Beaver,et al.  The Handbook of Logic and Language , 1997 .

[51]  Pierre Wolper,et al.  The tableau method for temporal logic: an overview , 1985 .

[52]  Henny B. Sipma,et al.  STeP: The Stanford Temporal Prover (Educational Release) User''s Manual , 1995 .

[53]  Michael Wooldridge,et al.  Resolution for Temporal Logics of Knowledge , 1998, J. Log. Comput..

[54]  Mark Steedman,et al.  In handbook of logic and language , 1997 .

[55]  Stefan Schwendimann,et al.  A New One-Pass Tableau Calculus for PLTL , 1998, TABLEAUX.