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A program-level approach to revising logic programs under the answer set semantics

Published online by Cambridge University Press:  09 July 2010

JAMES P. DELGRANDE
JAMES P. DELGRANDE*
Affiliation:
School of Computing Science, Simon Fraser University, Burnaby, B.C., CanadaV5A 1S6 (e-mail: jim@cs.sfu.ca)
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Abstract

An approach to the revision of logic programs under the answer set semantics is presented. For programs P and Q, the goal is to determine the answer sets that correspond to the revision of P by Q, denoted P * Q. A fundamental principle of classical (AGM) revision, and the one that guides the approach here, is the success postulate. In AGM revision, this stipulates that α ∈ K * α. By analogy with the success postulate, for programs P and Q, this means that the answer sets of Q will in some sense be contained in those of P * Q. The essential idea is that for P * Q, a three-valued answer set for Q, consisting of positive and negative literals, is first determined. The positive literals constitute a regular answer set, while the negated literals make up a minimal set of naf literals required to produce the answer set from Q. These literals are propagated to the program P, along with those rules of Q that are not decided by these literals. The approach differs from work in update logic programs in two main respects. First, we ensure that the revising logic program has higher priority, and so we satisfy the success postulate; second, for the preference implicit in a revision P * Q, the program Q as a whole takes precedence over P, unlike update logic programs, since answer sets of Q are propagated to P. We show that a core group of the AGM postulates are satisfied, as are the postulates that have been proposed for update logic programs.

Keywords

answer set programmingbelief changebelief revision
Type
Regular Papers
Information
Theory and Practice of Logic Programming , Volume 10 , Special Issue 4-6: 26th International Conference on Logic Programming , July 2010 , pp. 565 - 580
Copyright
Copyright © Cambridge University Press 2010

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References

Alchourrón, C., Gärdenfors, P., and Makinson, D. 1985. On the logic of theory change: Partial meet functions for contraction and revision. Journal of Symbolic Logic 50, 2, 510–530.CrossRefGoogle Scholar
Alferes, J. J., Leite, J. A., Pereira, L. M., Przymusinska, H., and Przymusinski, T. C. 2000. Dynamic updates of non-monotonic knowledge bases. Journal of Logic Programming 45, 1–3, 43–70.CrossRefGoogle Scholar
Baral, C. 2003. Knowledge Representation, Reasoning and Declarative Problem Solving. Cambridge University Press.CrossRefGoogle Scholar
Dalal, M. 1988. Investigations into theory of knowledge base revision. In Proceedings of the AAAI National Conference on Artificial Intelligence. St. Paul, Minnesota, 449–479.Google Scholar
Delgrande, J. and Schaub, T. 2003. A consistency-based approach for belief change. Artificial Intelligence 151, 1–2, 1–41.CrossRefGoogle Scholar
Delgrande, J., Schaub, T., Tompits, H., and Woltran, S. 2008. Belief revision of logic programs under answer set semantics. In Proceedings of the Eleventh International Conference on the Principles of Knowledge Representation and Reasoning, Brewka, G. and Lang, J., Eds. AAAI Press, Sydney, 411–421.Google 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, 711–767.CrossRefGoogle Scholar
Foo, N. and Zhang, Y. 1997. Towards generalized rule-based updates. In Proceedings of the Fifteenth International Joint Conference on Artificial Intelligence (IJCAI'97), Vol. 1. Morgan Kaufmann, 82–88.Google Scholar
Gärdenfors, P. 1988. Knowledge in Flux: Modelling the Dynamics of Epistemic States. MIT, Cambridge, MA.Google Scholar
Gebser, M., Kaufmann, B., Neumann, A., and Schaub, T. 2007. Conflict-driven answer set solving. In Proceedings of the Twentieth International Joint Conference on Artificial Intelligence (IJCAI'07), Veloso, M., Ed. AAAI Press/MIT, 386–392.Google Scholar
Gelfond, M. and Lifschitz, V. 1990. Logic programs with classical negation. In Proceedings of the International Conference on Logic Programming, Warren, D. H. D. and Szeredi, P., Eds. MIT, 579–597.Google Scholar
Inoue, K. and Sakama, C. 1999. Updating extended logic programs through abduction. In Proceedings of the Fifth International Conference on Logic Programming and Nonmonotonic Reasoning (LPNMR'99). Lecture Notes in Artificial Intelligence, vol. 1730. Springer, 147–161.Google Scholar
Leone, N., Pfeifer, G., Faber, W., Eiter, T., Gottlob, G., Perri, S., and Scarcello, F. 2006. The DLV system for knowledge representation and reasoning. ACM Transactions on Computational Logic 7, 3, 499–562.CrossRefGoogle Scholar
Lifschitz, V., Pearce, D., and Valverde, A. 2001. Strongly equivalent logic programs. ACM Transactions on Computational Logic 2, 4, 526–541.CrossRefGoogle Scholar
Satoh, K. 1988. Nonmonotonic reasoning by minimal belief revision. In Proceedings of the International Conference on Fifth Generation Computer Systems. Tokyo, 455–462.Google Scholar
Simons, P., Niemelä, I., and Soininen, T. 2002. Extending and implementing the stable model semantics. Artificial Intelligence 138, 1–2, 181–234.CrossRefGoogle Scholar
Tasharrofi, S. 2009. Belief revision through ASP programs. Unpublished manuscript.Google Scholar
Williams, M.-A. 1995. Iterated theory base change: A computational model. In Proceedings of the International Joint Conference on Artificial Intelligence. Montréal, 1541–1547.Google Scholar
Zhang, Y. and Foo, N. Y. 1998. Updating logic programs. In Proceedings of the Thirteenth European Conference on Artificial Intelligence (ECAI'98). 403–407.Google Scholar