Abstract
We propose a logic for partial reasoning over all general logic programs in a certain first-order language L. We need such a logic to express statements like it is impossible that a ground atom is both true and false in any program. To construct this logic we start with Kleene's three-valued logic. Then we extend L to a metalanguage L * by including a new system of connectives. Basing upon Kripke's approach we introduce the notion of truth for formulas of L *. Comparison with classical logic and intuitionistic one is given. We prove that every intuitionistic theorem is true in our logic. We also show how classical tautologies are mapped onto true formulas.
Research supported by Russian Fund for Fundamental Research Grant 93-012-590.
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References
Apt, K.R., Blair, H., and Walker, A. Towards a theory of declarative knowledge. In J.Minker, ed. Foundations of Deductive Databases and Logic Programming. Morgan-Kaufmann, Sun Mateo, Calif., 1988, pp. 89–148.
Apt, K.R., Logic Programming. In: J. van Leeuwen, ed. Handbook of Theoretical Computer Science, Elsevier Science Publishers B.V., 1990, pp. 495–574.
Clark, K.L. Negation as Failure. In: H.Gallaire and J.Minker (eds.), Logic and Databases, Plenum, New York, 1978, pp. 293–322.
Fitting, M. A Kripke-Kleene Semantics for Logic Programs, J. Logic Prog., 2:295–312 (1985).
Gelfond, M., and Lifschitz, V. The stable model semantics for logic programming. In Proceedings of the 5th International Conference and Symposium on Logic Programming (Seattle, Wash.). IEEE, New York, 1988, pp.1070–1080.
Kleene, S.C., Introduction to Metamathematics, Van Nostrand, New York, 1952.
Kripke, S.A. Semantical Analysis of Intuitionistic Logic I, In Formal Systems and Recursive Functions, Amsterdam, 1965, pp.92–129.
Kripke, S.A. Semantical Consideration on Model Logic. In L.Linsky, ed. Reference and Modality, Oxford University Press, London, pp.63–72, 1971.
Kunen, K. Negation in Logic Programming, J. Logic Prog., 4:289–308 (1987).
Kuznetsov, V. Negation as Exception. In B.Neumann, ed. Proceedings of the 10th European Conference on Artificial Intelligence (Vienna). John Wiley and Sons, 1992, pp.107–108.
Martin-Löf, P. Notes on Constructive Mathematics. Almqvist & Wiksell, Stockholm, 1970.
Przymusinski, T.C. On the declarative semantics of deductive databases and logic programs. In J.Minker, ed. Foundations of Deductive Databases and Logic Programming. Morgan-Kaufmann, Sun Mateo, Calif., 1988, pp. 193–216.
Przymusinski, T.C. The Well-Founded Semantics Coincides with the Three-Valued Stable Model Semantics, Fundamenta Informaticae, 13:445–464 (1990).
Smullyan, R.M. Theory of Formal Systems, revised edition, Princeton U.P., Princeton, 1961.
Van Gelder, A., Ross, K.A., and Schlipf J.S. The Well-Founded Semantics for General Logic Programs, J. ACM, 38:620–650 (1991).
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Kuznetsov, V. (1994). A Kripke-Kleene logic over general logic programs. In: Nebel, B., Dreschler-Fischer, L. (eds) KI-94: Advances in Artificial Intelligence. KI 1994. Lecture Notes in Computer Science, vol 861. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-58467-6_7
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DOI: https://doi.org/10.1007/3-540-58467-6_7
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