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Updates in answer set programming: An approach based on basic structural properties

Published online by Cambridge University Press:  01 July 2007

MAURICIO OSORIO
Affiliation:
Universidad de las Américas Puebla, Sta. Catarina Mártir, Cholula, Puebla, 72820, México (e-mail: [email protected], [email protected]
VÍCTOR CUEVAS
Affiliation:
Universidad de las Américas Puebla, Sta. Catarina Mártir, Cholula, Puebla, 72820, México (e-mail: [email protected], [email protected]

Abstract

We have studied the update operator ⊕1 defined for update sequences by Eiter et al. without tautologies and we have observed that it satisfies an interesting property. This property, which we call Weak Independence of Syntax (WIS), is similar to one of the postulates proposed by Alchourrón, Gärdenfors, and Makinson (AGM); only that in this case it applies to nonmonotonic logic. In addition, we consider other five additional basic properties about update programs and we show that ⊕1 satisfies them. This work continues the analysis of the AGM postulates with respect to the ⊕1 operator under a refined view that considers N2 as a monotonic logic which allows us to expand our understanding of answer sets. Moreover, N2 helped us to derive an alternative definition of ⊕1 avoiding the use of unnecessary extra atoms.

Type
Regular Papers
Copyright
Copyright © Cambridge University Press 2007

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References

Alchourrón, C. E., Gärdenfors, P., and Makinson, D. 1985. On the logic of theory change: Partial meet functions for contraction and revision. Journal of Symbolic Logic 50: 510530.CrossRefGoogle Scholar
Alferes, J. J. and Pereira, L. M. 2002. Logic programming updating - a guided approach. Computational Logic: Logic Programming and Beyond, Essays in Honour of Robert A. Kowalski, Part II. Springer-Verlag, pp. 382412.CrossRefGoogle Scholar
Banti, F., Alferes, J. J. and Brogi, A. 2003. A principled semantics for logic program updates. In Nonmonotonic Reasoning, Action, and Change (NRAC'03), Brewka and Peppas, Eds.Google Scholar
Banti, F., Alferes, J. J. and Brogi, A. 2005. Operational semantics for dylps. Progress in Artificial Intelligence: 12th Portuguese Conference on Artificial Intelligence, EPIA 2005. Covilhã, Portugal.Google Scholar
Baral, C. 2003. Knowledge Representation, Reasoning and Declarative Problem Solving. Cambridge University Press.CrossRefGoogle Scholar
Eiter, T., Fink, M., Sabbatini, G. and Tompits, H. 2002. On properties of update sequences based on causal rejection. Theory and Practice of Logic Programming 2, 6, 711767.CrossRefGoogle Scholar
Ferraris, P. and Lifschitz, V. 2005. Weight constraints as nested expressions. Theory and Practice of Logic Programming 5, 4574.CrossRefGoogle Scholar
Gelfond, M. and Lifschitz, V. 1988. The stable model semantics for logic programming. 5th Conference on Logic Programming, Kowalski, R. and Bowen, K., Eds. MIT Press, pp. 10701080.Google Scholar
Gelfond, M. and Lifschitz, V. 1991. Classical negation in logic programs and disjunctive databases. New Generation Computing 9,(3/4): 365386.CrossRefGoogle Scholar
Gurevich, Y. 1977. Intuitionistic logic with strong negation. Studia Logica 36: 4959.CrossRefGoogle Scholar
Homola, M. 2005. Dynamic logic programming: Various semantics are equal on acyclic programs. Computational Logic in Multi-Agent Systems: 5th International Workshop, CLIMA V, Leite, J. and Torroni, P., Eds. Number 3487 in Lecture Notes in Computer Science. Springer, pp. 7895.CrossRefGoogle Scholar
Katsuno, H. and Mendelzon, A. O. 1991. Propositional knowledge base revision and minimal change. Artificial Intelligence 52, 3: 263294.CrossRefGoogle Scholar
Katsuno, H. and Mendelzon, A. O. 1992. On the difference between updating a knowledge base and revising it. Belief Revision, Gärdenfors, P., Ed. Cambridge University Press, 183203.CrossRefGoogle Scholar
Kracht, M. 1998. On extensions of intermediate logics by strong negation. Journal of Philosophical Logic: 49–73.CrossRefGoogle Scholar
Lifschitz, V., Pearce, D. and Valverde, A. 2001. Strongly equivalent logic programs. ACM Transactions on Computational Logic 2: 526541.CrossRefGoogle Scholar
Lifschitz, V., Tang, L. R., and Turner, H. 1999. Nested expressions in logic programs. Annals of Mathematics and Artificial Intelligence 25: 369389.CrossRefGoogle Scholar
Mendelson, E. 1987. Introduction to Mathematical Logic, Third ed. Wadsworth, Belmont, CA.CrossRefGoogle Scholar
Nelson, D. 1949. Constructible falsity. Journal of Symbolic Logic 14: 1626.CrossRefGoogle Scholar
Ortiz, M. and Osorio, M. 2005. Nelson's strong negation, safe beliefs and the answer sets semantics. In Answer Set Programming: Advances in Theory and Implementation ASP'05. Bath, UK, pp. 7084.Google Scholar
Osorio, M., Navarro, J. A. and Arrazola, J. 2001. Equivalence in answer set programming. In Logic Based Program Synthesis and Transformation. 11th International Workshop, LOPSTR 2001, Pettorossi, A., Ed. Number 2372 in Lecture Notes in Computer Science. Springer, Paphos, Cyprus, pp. 5775.Google Scholar
Osorio, M., Navarro, J. A. and Arrazola, J. 2004. Applications of intuitionistic logic in answer set programming. Theory and Practice of Logic Programming 4, 3: 325354.CrossRefGoogle Scholar
Osorio, M., Navarro, J. A. and Arrazola, J. 2005a. Safe beliefs for propositional theories. Annals of Pure and Applied Logic 134, 1: 6382.CrossRefGoogle Scholar
Osorio, M., Navarro, J. A. and Arrazola, J. 2005b. Safe beliefs for propositional theories. Annals of Pure and Applied Logic 134, 1: 6382.CrossRefGoogle Scholar
Osorio, M. and Zacarías, F. 2003. Irrelevance of syntax in updating answer set programs. Proceedings of the Fourth Mexican International Conference on Computer Science (ENC'03) Workshop on Logic and Agents. Apizaco, México.Google Scholar
Osorio, M. and Zacarías, F. 2004. On updates of logic programs: a properties–based approach. Proceedings of the Third International Symposium on Foundations of Information and Knowledge Systems (FoIKS 2004), Seipel, D. and Turrul, J., Eds., pp. 231241.Google Scholar
Pearce, D. 1999a. From here to there: Stable negation in logic programming. In What Is Negation?, Gabbay, D. M. and Wansing, H., Eds. Kluwer Academic Publishers, Netherlands, pp. 161181.CrossRefGoogle Scholar
Pearce, D. 1999b. Stable inference as intuitionistic validity. Logic Programming 38: 7991.CrossRefGoogle Scholar
Rasiowa, H. 1974. An Algebraic Approach to Non-Classical Logics. Elsevier.Google Scholar
van Dalen, D. 1986. Intuitionistic logic handbook of philosophical logic. In Alternatives to Classical Logic, Gabbay, D. and Guenthner, F., Eds. Vol. 3 D. Reidel.Google Scholar
Vorob'ev, N. 1952a. Constructive propositional calculus with strong negation. Doklady Akademii Nauk SSSR 85, pp. 465468. In Russian.Google Scholar
Vorob'ev, N. 1952b. The problem of deducibility in constructive propositional calculus with strong negation. Doklady Akademii Nauk SSSR 85, pp. 689692. In Russian.Google Scholar