Abstract
In order to really understand all aspects of logic-based program development of different semantics, it would be useful to have a common solid logical foundation.
The stable semantics are based on G 3 but we show that stable semantics can be fully represented in the three valued logic of Łukasiewicz . We construct a particular semantics that we call Ł3-WFS which is defined over general propositional theories, can be defined via three valued logic of Łukasiewicz. Interesting Ł3-WFS seems to satisfy most of the principles of a well behaved semantics. Hence we propose the three valued Łukasiewicz logic to model WFS, extensions of WFS, and the Stable semantics.
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References
Apt, K., Blair, H.A., Walker, A.: Towards a Theory of declarative Knowledge. In: Minker, J. (ed.) Fundations of deductive data bases, vol. 89, p. 148. Morgan Kaufmann, San Francisco (1988)
Brewka, G., Dix, J., Konolige, K.: Non Monotonic Reasoning An Overview. Center for the Study of Languages and Information Stanford California (1997)
Arnon, A.: On the Expressive Power of the Three-Valued and FOUR-Valued Languages. Journal of Logic and Computation 9 (1999)
Arnon, A.: Natural 3-valued Logics-Characterization and Proof Theory. Journal of Symbolic Logic 56, 276–294 (1991)
Denecker, M., Pelov, N., Bruynooghe, M.: Ultimate Well-Founded and Stable Semantics for Logic Programs with Aggregates. In: Codognet, P. (ed.) ICLP 2001. LNCS, vol. 2237, pp. 212–226. Springer, Heidelberg (2001)
Dix, J.: A Classification Theory of Semantics of Normal Logic Programs: I. Strong Properties. Fundamental Informaticae XXII (3), 227–255 (1995)
Dix, J.: A Classification Theory of Semantics of Normal Logic Programs: II. Weak Properties. Fundamental Informaticae XXII (3), 257–288 (1995)
Dix, J., Osorio, M., Zepeda, C.: A general theory of confluent rewriting systems for logic programming and its applications. Annals of Pure and Applied Logic 108(1–3),153–188 (2001)
Font, J.M., Hajek, P.: Lukasiewicz and modal logic (Preprints)
Gelfond, M.: On stratified auto-epistemic theories. In: Proceedings of AAAI 1887, pp. 207–211. Morgan Kaufmann, San Francisco (1987)
Gelfond, M., Lifschitz, V.: The stable model semantics for logic programs. In: Proceedings of the Fifth International Conference on Logic Programming, pp. 1070–1080. MIT Press, Cambridge (1988)
Lifschitz, V., Pearce, D., Valverde, A.: Strongly equivalent logic programs. ACM Transactions on Computational Logic 2, 526–541 (2001)
McDermott, D.: Nonmonotonic Logic II: nonmonotonic Modal Theories. Journal of the Association for Computing Machinery 29(1), 33–57 (1982)
Minari, P.: A note on Lukasiewicz’s three-valued logic. Essay from Pierluigi Minari. Dept. of Philosophy, University of Florence
Osorio, M., Borja, V., Arrazola, J.: Closing the Gap between the Stable Semantics and Extensions of WFS. In: Monroy, R., Arroyo-Figueroa, G., Sucar, L.E., Sossa, H. (eds.) MICAI 2004. LNCS (LNAI), vol. 2972, pp. 202–211. Springer, Heidelberg (2004)
Osorio, M., Navarro, J.A., Arrazola, J.: Applications of Intuitionistic Logic in Answer Set Programming. accepted in Journal of TPLP (2003)
Osorio, M., Navarro, J.A., Arrazola, J.: A Logical Approach to A-prolog. In: 9th. Workshop on Logic Language and Information, Brazil (2002)
Pearce, D.: Stable inference as intuitionistic validity. The Journal of Logic Programming 38, 79–91 (1999)
Schlipf, J.S.: Formalizing a Logic for Logic Programming. Annals of Mathematics and Artificial Intelligence 5, 279–302 (1992)
van Gelder, A., Ross, K.A., Schlipf, J.S.: The well-founded semantics for general logic programs. Journal of the ACM 38, 620–650 (1991)
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Osorio, M., Borja, V., Arrazola, J. (2004). Three Valued Logic of Łukasiewicz for Modeling Semantics of Logic Programs. In: Lemaître, C., Reyes, C.A., González, J.A. (eds) Advances in Artificial Intelligence – IBERAMIA 2004. IBERAMIA 2004. Lecture Notes in Computer Science(), vol 3315. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30498-2_35
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DOI: https://doi.org/10.1007/978-3-540-30498-2_35
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