Strong and uniform equivalence of nonmonotonic theories-An algebraic approach

Proceedings of the International Conference on Knowledge Representation and Reasoning

Volumn , Issue , 2006, Pages 389-399

  Truszczyński, Mirosław ^a  

^a UNIVERSITY OF KENTUCKY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALGEBRA; FORMAL LOGIC; KNOWLEDGE REPRESENTATION; LOGIC PROGRAMMING;

ALGEBRAIC APPROACHES; COMPLETE LATTICES; DEFAULT LOGIC; LOGIC PROGRAMS; NONMONOTONIC; NONMONOTONIC LOGIC;

COMPUTER CIRCUITS;

EID: 84860566884     PISSN: 23341025     EISSN: 23341033     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (26)

1. Denecker, M.; Marek, V.; and Truszczyński, M. 2000. Approximations, stable operators, well-founded fixpoints and applications in nonmonotonic reasoning. In Minker, J., ed., Logic-Based Artificial Intelligence. Kluwer Academic Publishers. 127-144.
2. Denecker, M.; Marek, V.; and Truszczyński, M. 2003. Uniform semantic treatment of default and autoepistemic logics. Artificial Intelligence Journal 143:79-122.
3. Eiter, T., and Fink, M. 2003. Uniform equivalence of logic programs under the stable model semantics. In Proceedings of the 2003 International Conference on Logic Programming, volume 2916 of Lecture Notes in Computer Science, 224-238. Berlin: Springer.
4. Eiter, T.; Fink, M.; and Woltran, S. 2006. Semantical characterizations and complexity of equivalences in answer set programming. ACM Transactions on Computational Logic. To appear.
5. Fitting, M. C. 1985. A Kripke-Kleene semantics for logic programs. Journal of Logic Programming 2(4):295-312.
6. Fitting, M. 1991. Bilattices and the semantics of logic programming. Journal of Logic Programming 11:91-116.
7. Fitting, M. C. 2002. Fixpoint semantics for logic programming - a survey. Theoretical Computer Science 278:25-51.
8. Gelfond, M., and Lifschitz, V. 1988. The stable semantics for logic programs. In Proceedings of the 5th International Conference on Logic Programming, 1070-1080. MIT Press.
9. Gelfond, M., and Lifschitz, V. 1991. Classical negation in logic programs and disjunctive databases. New Generation Computing 9:365-385.
10. Ginsberg, M. 1988. Multivalued logics: a uniform approach to reasoning in artificial intelligence. Computational Intelligence 4:265-316.
11. Heyting, A. 1930. Die formalen regeln der intuitionistischen logik. Sitzungsberichte der Preussischen Akademie von Wissenschaften. Physikalisch-mathematische Klasse 42-56.
12. Lifschitz, V.; Pearce, D.; and Valverde, A. 2001. Strongly equivalent logic programs. ACM Transactions on Computational Logic 2(4):526-541.
13. Lifschitz, V.; Tang, L. R.; and Turner, H. 1999. Nested expressions in logic programs. Annals of Mathematics and Artificial Intelligence 369-389.
14. Lin, F. 2002. Reducing strong equivalence of logic programs to entailment in classical propositional logic. In Principles of Knowledge Representation and Reasoning, Proceedings of the 8th International Conference (KR2002). Morgan Kaufmann Publishers.
15. Marek, W., and Truszczyński, M. 1993. Nonmonotonic Logic; Context-Dependent Reasoning. Berlin: Springer.
16. Pearce, D., and Valverde, A. 2004. Uniform equivalence for equilibrium logic and logic programs. In Proceedings of the 7th International Conference on Logic Programming and Nonmonotonic Reasoning, volume 2923 of Lecture Notes in Artificial Intelligence, 194-206. Springer.
17. Pelov, N., and Truszczyński, M. 2004. Semantics of disjunctive programs with monotone aggregates - an operator-based approach. In Delgrande, J., and Schaub, T., eds., Proceedings of the 10th International Workshop on Non-Monotonic Reasoning, NMR-04, 327-334.
18. th International Conference, volume 2923, 207-219. Springer.
19. Pelov., N. 2004. Semantics of logic programs with aggregates. PhD Thesis. Department of Computer Science, K.U.Leuven, Leuven, Belgium.
20. Reiter, R. 1980. A logic for default reasoning. Artificial Intelligence 13(1-2):81-132.
21. Tarski, A. 1955. Lattice-theoretic fixpoint theorem and its applications. Pacific Journal of Mathematics 5:285-309.
22. Turner, H. 2001. Strong equivalence for logic programs and default theories (made easy). In Proceedings of Logic Programming and Nonmonotonic Reasoning Conference, LPNMR 2001, volume 2173, 81-92. Lecture Notes in Artificial Intelligence, Springer.
23. Turner, H. 2003. Strong equivalence made easy: Nested expressions and weight constraints. Theory and Practice of Logic Programming 3, (4&5):609-622.
24. van Emden, M., and Kowalski, R. 1976. The semantics of predicate logic as a programming language. Journal of the ACM 23(4):733-742.
25. Vennekens, J.; Gilis, D.; and Denecker, M. 2004a. Splitting an operator: An algebraic modularity result and its application to auto-epistemic logic. In Delgrande, J., and Schaub, T., eds., Proceedings of the 10th International Workshop on Non-Monotonic Reasoning, 400-408.
26. Vennekens, J.; Gilis, D.; and Denecker, M. 2004b. Splitting an operator: an algebraic modularity result and its applications to logic programming. In Lifschitz, V., and Demoen, B., eds., Logic programming, Proceedings of the 20th International Conference on Logic Programming, ICLP-04, 195-209.