Abstract
This paper is concerned with the definition of strategies for resolution in modal logic. We propose the following strategies: deletion of subsumed clauses, extensions of classical strategies based on a static constraint, negative resolution, input and linear resolution. A class of strategies based on static constraints and the linear strategy are proved to be complete. For input and negative strategy we have completeness results provided some restrictions on the class of considered clauses. Some problems such as completeness of deletion of subsumed clauses are left open; we state and discuss them in the paper.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Abadi, M. and Manna, Z., ‘Non-clausal temporal deduction’, in Logics of Programs (R. Parikh, ed.), Springer-Verlag Lecture Notes in Computer Science 173, 1985, pp. 1–15.
Chang, C. and Lee, R., Symbolic Logic and Mechanical Theorem Proving, Academic Press, 1973.
Cialdea, M., ‘Une méthode de déduction automatique en logique modale’, Thèse de l'Université P. Sabatier, Toulouse, 1986.
Enjalbert, P. and Farinas, L., ‘Modal resolution in clausal form’, to appear in Theor. Comput. Sci., 1989.
Farinas del Cerro, L., ‘Resolution modal logic, Logique et Analyse, no. 110, 111, 1985, pp. 152–172.
Farinas del Cerro, L., ‘Molog, a system that extends PROLOG with modal logic’, New Generation Computing, 4, 35–50 (1986).
Farinas del Cerro L. and Pentonen M., ‘A note on the complexity of satisfiability of modal Horn clauses’, J. of Logic Program, 4 (1), March 1987.
Hughes, G. E. and Cresswell, H. J., An Introduction to Modal Logic, Methuen, 1968.
Konolidge, K., ‘A resolution method for quantified modal logics of knowledge and belief’, Proc. 1986 Conference on Reasoning about Knowledge (J. Y. Halpern, ed.), pp. 309–324.
Loveland, D. W., Automated Theorem Proving: A Logical Basis, North Holland, 1978.
McCarthy, J. et al., On the Modal Theory of Knowledge, Memorandum AIM-312, Stanford University, 1978.
Okada, M., ‘Mathematical basis of modal logic programming’, Journées Européennes sur les méthodes Logiques en Intelligence Artificielle, Roscoff, France, 1988.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Auffray, Y., Hebrard, JJ. Strategies for modal resolution: Results and problems. J Autom Reasoning 6, 1–38 (1990). https://doi.org/10.1007/BF00302639
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF00302639