Abstract
In a previous work we have defined Monotonic Logic Programs which extend definite logic programming to arbitrary complete lattices of truth-values with an appropriate notion of implication. We have shown elsewhere that this framework is general enough to capture Generalized Annotated Logic Programs, Probabilistic Deductive Databases, Possibilistic Logic Programming, Hybrid Probabilistic Logic Programs and Fuzzy Logic Programming [3],[4]. However, none of these semantics define a form of non-monotonic negation, which is fundamental for several knowledge representation applications. In the spirit of our previous work, we generalise our framework of Monotonic Logic Programs to allow for rules with arbitrary antitonic bodies over general complete lattices, of which normal programs are a special case. We then show that all the standard logic programming theoretical results carry over to Antitonic Logic Programs, defining Stable Model and Well-founded Model alike semantics. We also apply and illustrate our theory to logic programs with costs, extending the original presentation of [17] with a class of negations.
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References
C. Baral and V. S. Subrahmanian. Duality between alternative semantics of logic programs and nonmonotonic formalisms. Journal of Automated Reasoning, 10:399–420, 1993. 389
L. Bolc and P. Borowik. Many-Valued Logics. Theoretical Foundations. Springer-Verlag, 1992. 391
C. V. Damásio and L. M. Pereira. Hybrid probabilistic logic programs as residuated logic programs. In M. O. Aciego, I. P. de Guzmán, G. Brewka, and L. M. Pereira, editors, Proc. of JELIA’00, pages 57–72. LNAI 1919, Springer-Verlag, 2000. 379
C. V. Damásio and L. M. Pereira. Monotonic and residuated logic programs, 2001. Accepted in ECSQARU-2001. 379, 381
A. Dekhtyar and V. S. Subrahmanian. Hybrid probabilistic programs. In International Conference on Logic Programming 1997, pages 391–495. MIT Press, 1997. 379
M. Denecker, V. Marek, and M. Truszczyński. Approximations, stable operators, well-founded fixpoints and applications in nonmonotonic reasoning. In J. Minker, editor, Logic-Based Artifical Intelligence, pages 127–144. Kluwer Academic Publishers, 2000. 380, 391
D. Dubois, J. Lang, and H. Prade. Towards possibilistic logic programming. In International Conference on Logic Programming 1991, pages 581–598. MIT Press, 1991. 379
M. Fitting. Bilattices and the semantics of logic programs. Journal of Logic Programming, 11:91–116, 1991. 379, 391
M. Fitting. The family of stable models. Journal of Logic Programming, 17:197–225, 1993. 379, 391
J. H. Gallier. Logic for Computer Science. John Wiley & Sons, 1987. 381, 382
A. Van Gelder, K. A. Ross, and J. S. Schlipf. The well-founded semantics for general logic programs. Journal of the ACM, 38(3):620–650, 1991. 385
M. Gelfond and V. Lifschitz. The stable model semantics for logic programming. In R. Kowalski and K. A. Bowen, editors, 5th International Conference on Logic Programming, pages 1070–1080. MIT Press, 1988. 385, 386
P. Hájek. Metamathematics of Fuzzy Logic. Trends in Logic. Studia Logica Library. Kluwer Academic Publishers, 1998. 391
M. Kifer and V. S. Subrahmanian. Theory of generalized annotated logic programming and its applications. J. of Logic Programming, 12:335–367, 1992. 379, 391
R. Kowalski. Predicate logic as a programming language. In Proceedings of IFIP’74, pages 569–574. North Holland Publishing Company, 1974. 380
J. W. Lloyd. Foundations of Logic Programming. Springer-Verlag, 1987. 380
V. W. Marek and M. Truszczyński. Logic programming with costs. Technical report, 2000. Available at ftp://al.cs.engr.uky.edu/cs/manuscripts/lp-costs.ps. 379, 380, 383, 385, 390, 391
J. Medina, M. Ojeda-Aciego, and P. Vojtas. Multi-adjoint logic programming with continuous semantics. In Proc. of LPNMR’01, September 2001. This issue. 384
H. Przymusinska and T. C. Przymusinski. Semantic issues in deductive databases and logic programs. In R. Banerji, editor, Formal Techniques in Artificial Intelligence, a Sourcebook, pages 321–367. North Holland, 1990. 387
V. S. Subrahmanian. Algebraic properties of the space of multivalued and paraconsistent logic programs. In 9th Int. Conf. on Foundations of Software Technology and Theoretical Computer Science, pages 56–67. LNCS 405, Springer-Verlag, 1989. 379, 391
M. van Emden and R. Kowalski. The semantics of predicate logic as a programming language. Journal of ACM, 4(23):733–742, 1976. 380, 383
M. H. van Emden. Quantitative deduction and its fixpoint theory. Journal of Logic Programming, 4:37–53, 1986. 380, 391
P. Vojtás. Fuzzy logic programming. Fuzzy Sets and Systems, 2001. Accepted. 379
P. Vojtás and L. Paulík. Soundness and completeness of non-classical extended SLD-resolution. InProc. of theWs. on Extensions of Logic Programming (ELP’96), pages 289–301. LNCS 1050, Springer-Verlag., 1996. 379
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Damásio, C.V., Pereira, L.M. (2001). Antitonic Logic Programs. In: Eiter, T., Faber, W., Truszczyński, M.l. (eds) Logic Programming and Nonmotonic Reasoning. LPNMR 2001. Lecture Notes in Computer Science(), vol 2173. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45402-0_28
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DOI: https://doi.org/10.1007/3-540-45402-0_28
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