Abstract
We present a logic programming language, which we call Proflog, with an operational semantics based on tableaux and a denotational semantics based on supervaluations. We show the two agree. Negation is well behaved, and semantic noncomputability issues do not arise. This is accomplished essentially by dropping a domain closure requirement. The cost is that intuitions developed through the use of classical logic may need modification, though the system is still classical at a level once removed. Implementation problems are discussed very briefly; the thrust of the paper is primarily theoretical.
Similar content being viewed by others
References
Bowen, K. A.: Programming with full first-order logic, in Hayes, Michie, and Pao (eds),Michine Intelligence, vol. 10, Ellis Horwood and John Wiley, 1982, pp. 421–440.
Fitting, M. C.: A Kripke/Kleene semantics for logic programs,J. Logic Programming 2 (1985), 295–312.
Fitting, M. C.: Partial models and logic programming,Theoretical Computer Science 48 (1987), 229–255.
Fitting, M. C.:First-Order Logic and Automated Theorem Proving, Springer-Verlag, 1990.
Gelfond, M. and Lifschitz, V.: The stable model semantics for logic programming, in R. Kowalski and K. Bowen (eds),Proc. of the Fifth Logic Programming Symposium, MIT Press, 1988, pp. 1070–1080.
Kunen, K.: Negation in logic programming,J. Logic Programming 4 (1987), 289–308.
Kunen, K.: Signed data dependencies in logic programming,J. Logic Programming 7 (1989), 231–245.
Moschovakis, Y. N.:Elementary Induction on Abstract Structures, North-Holland, 1974.
Schönfeld, W.: Prolog extensions based on tableau calculus, inProc. of the Ninth Int. Joint. Conf. on Artificial Intelligence, 1985, pp. 730–732.
Smullyan, R. M.:First-Order Logic, Springer-Verlag, 1968.
Van Fraassen, B.: Singular terms, truth-value gaps, and free logic,J. Philosophy 63 (1966), 481–485.
Van Gelder, A., Ross, K. A., and Schlipf, J. S.: The well-founded semantics for general logic programs,JACM 38 (1991), 620–650.
Author information
Authors and Affiliations
Additional information
Research partly supported by NSF Grant CCR-9104015.
Rights and permissions
About this article
Cite this article
Fitting, M. Tableaux for logic programming. J Autom Reasoning 13, 175–188 (1994). https://doi.org/10.1007/BF00881954
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00881954