Abstract
In this paper, we present algorithms developed in order to implement a clausal resolution method for discrete, linear temporal logics, presented in [Fis91]. As part of this method, temporal formulae are rewritten into a normal form and both ‘non-temporal’ and ‘temporal’ inference rules are applied. Through the use of a graph-based representation for the normal form, “efficient” search algorithms can be applied to detect sets of formulae for which temporal resolution is applicable. Further, rather than constructing the full graph structure, our algorithms only explore and construct as little of the graph as possible. These algorithms have been implemented and have been combined with sub-programs performing translation to normal form and non-temporal resolution to produce an integrated resolution based temporal theorem-prover.
The work of the first author was supported by SERC under a PhD Studentship.
Preview
Unable to display preview. Download preview PDF.
References
M. Abadi. Temporal-Logic Theorem Proving. PhD thesis, Department of Computer Science, Stanford University, March 1987.
M. Abadi and Z. Manna. Nonclausal Deduction in First-Order Temporal Logic. ACM Journal, 37(2):279–317, April 1990.
H. Barringer, M. Fisher, D. Gabbay, G. Gough, and R. Owens. MetateM: A Framework for Programming in Temporal Logic. In Proceedings of REX Workshop on Stepwise Refinement of Distributed Systems: Models, Formalisms, Correctness, Mook, Netherlands, June 1989.
A. Cavali and L. Fariñas del Cerro. A Decision Method for Linear Temporal Logic. In R. E. Shostak, editor, Proceedings of the 7th International Conference on Automated Deduction, pages 113–127. LNCS 170, 1984.
C-L. Chang and R. Lee. Symbolic Logic and Mechanical Theorem Proving. Academic Press, 1973.
M. Carlsson and J. Widen. SICStus Prolog User's Manual. Swedish Institute of Computer Science, Kista, Sweden, September 1991.
C. Dixon. A graph-based approach to resolution in temporal logic. Master's thesis, Department of Computer Science, University of Manchester, Oxford Road, Manchester, December 1992.
P. Enjalbert and L. Fariñas del Cerro. Modal Resolution in Clausal Form. Theoretical Computer Science, 65:1–33, 1989.
M. Fisher. A Resolution Method for Temporal Logic. In Proceedings of the Twelfth International Joint Conference on Artificial Intelligence (IJCAI), Sydney, Australia, August 1991. Morgan Kaufman.
M. Fisher. A Normal Form for First-Order Temporal Formulae. In Proceedings of Eleventh International Conference on Automated Deduction (CADE), Saratoga Springs, New York, June 1992.
M. Fisher and P. Noël. Transformation and Synthesis in MetateM — Part I: Propositional MetateM. Technical Report UMCS-92-2-1, Department of Computer Science, University of Manchester, Oxford Road, Manchester M13 9PL, U.K., February 1992.
G. D. Gough. Decision Procedures for Temporal Logic. Master's thesis, Department of Computer Science, University of Manchester, October 1984.
D. Loveland. Automated Theorem Proving: a Logical Basis. North-Holland, Inc., 1978.
G. Mints. Gentzen-Type Systems and Resolution Rules, Part I: Prepositional Logic. Lecture Notes in Computer Science, 417:198–231, 1990.
H-J. Ohlbach. A Resolution Calculus for Modal Logics. Lecture Notes in Computer Science, 310:500–516, May 1988.
Martin Peim. Propositional Temporal Resolution Over Labelled Transition Systems. (Unpublished Technical Note), 1994.
S. Safra and M. Y. Vardi. On ω-Automata and Temporal Logic. In STOC, pages 127–137, Seattle, Washington, May 1989. ACM.
G. Venkatesh. A Decision Method for Temporal Logic based on Resolution. Lecture Notes in Computer Science, 206:272–289, 1986.
M. Vardi and P. Wolper. Automata-theoretic Techniques for Modal Logics of Programs. Journal of Computer and System Sciences, 32(2):183–219, April 1986.
P. Wolper. Temporal Logic Can Be More Expressive. Information and Control, 56, 1983.
L. Wos, R. Overbeek, E. Lusk, and J. Boyle. Automated Reasoning — Introduction and Applications. Prentice-Hall, Englewood Cliffs, New Jersey, 1984.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1994 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Dixon, C., Fisher, M., Barringer, H. (1994). A graph-based approach to resolution in temporal logic. In: Gabbay, D.M., Ohlbach, H.J. (eds) Temporal Logic. ICTL 1994. Lecture Notes in Computer Science, vol 827. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0014002
Download citation
DOI: https://doi.org/10.1007/BFb0014002
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-58241-0
Online ISBN: 978-3-540-48585-8
eBook Packages: Springer Book Archive