Strong and uniform equivalence of nonmonotonic theories - An algebraic approach

Annals of Mathematics and Artificial Intelligence

Volumn 48, Issue 3-4, 2006, Pages 245-265

  Truszczyński, Mirosław ^a  

^a UNIVERSITY OF KENTUCKY   (United States)

Author keywords

Autoepistemic logic; Default logic; Nonmonotonic theories

Indexed keywords

EID: 34347218262     PISSN: 10122443     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10472-007-9049-2     Document Type: Article

References (26)

1. Denecker, M., Marek, V., Truszczyński, M.: Approximations, stable operators, well-founded fixpoints and applications in nonmonotonic reasoning. In: Minker, J. (eds.) Logic-based Artificial Intelligence, pp. 127-144. Kluwer (2001)
2. Denecker, M., Marek, V., Truszczyński, M.: Uniform semantic treatment of default and autoepistemic logics. A. Int. J. 143, 79-122 (2003)
3. Eiter, T., Fink, M.: Uniform equivalence of logic programs under the stable model semantics. In: Proceedings of the 2003 International Conference on Logic Programming. Lecture Notes in Computer Science, vol. 2916, pp. 224-238. Springer, Berlin Heidelberg New York (2003)
4. Eiter, T., Fink, M., Woltran, S.: Semantical characterizations and complexity of equivalences in answer set programming. ACM Trans. Computat. Log. in press (July 2007)
5. Fitting, M.C.: A Kripke-Kleene semantics for logic programs. J. Log. Program. 2(4), 295-312 (1985)
6. Fitting, M.C.: Bilattices and the semantics of logic programming. J. Log. Program. 11, 91-116 (1991)
7. Fitting, M.C.: Fixpoint semantics for logic programming - a survey. Theor. Comp. Sci. 278, 25-51 (2002)
8. Ginsberg, M.L.: Multivalued logics: a uniform approach to reasoning in artificial intelligence. Comput. Intell. 4, 265-316 (1988)
9. Gelfond, M. Lifschitz, V.: The stable semantics for logic programs. In: Proceedings of the 5th International Conference on Logic Programming, pp. 1070-1080. MIT Press (1988)
10. Gelfond, M. Lifschitz, V.: Classical negation in logic programs and disjunctive databases. New Gener. Comput. 9, 365-385 (1991)
11. Heyting, A.: Die formalen regeln der intuitionistischen logik. Sitzungsberichte der Preussischen Akademie von Wissenschaften. Physikalisch-mathematische Klasse, pp. 42-56 (1930)
12. Lin, F.: Reducing strong equivalence of logic programs to entailment in classical prepositional logic. In: Principles of Knowledge Representation and Reasoning, Proceedings of the 8th International Conference (KR2002). Morgan Kaufmann (2002)
13. Lifschitz, V., Pearce, D., Valverde, A.: Strongly equivalent logic programs. ACM Trans. Comput. Log. 2(4), 526-541 (2001)
14. Lifschitz, V., Tang, L.R., Turner, H.: Nested expressions in logic programs. Ann. Math. Artif. Intell., 369-389 (1999)
15. Marek, W., Truszczyński, M.: Nonmonotonic Logic; Context-dependent Reasoning. Springer, Berlin (1993)
16. th International Conference, vol. 2923, pp. 207-219. Springer. Berlin Heidelberg New York (2004)
17. Pelov, N.: Semantics of logic programs with aggregates. Ph.D. thesis. Department of Computer Science, K.U.Leuven, Leuven, Belgium (2004)
18. Pelov, N.Truszczyński, M.: Semantics of disjunctive programs with monotone aggregates - an operator-based approach. In: Delgrande, J.P. Schaub, T. (eds.) Proceedings of the 10th International Workshop on Non-monotonic Reasoning, NMR-04, pp. 327-334 (2004)
19. Pearce, D. Valverde, A.: Uniform equivalence for equilibrium logic and logic programs. In: Proceedings of the 7th International Conference on Logic Programming and Nonmonotonic Reasoning. Lecture Notes in Artificial Intelligence, vol. 2923, pp. 194-206. Springer, Berlin Heidelberg New York (2004)
20. Reiter, R.: A logic for default reasoning. Artif. Intell. 13(1-2), 81-132 (1980)
21. Tarski, A.: Lattice-theoretic fixpoint theorem and its applications. Pac. J. Math. 5, 285-309 (1955)
22. Turner, H.: Strong equivalence for logic programs and default theories (made easy). In: Proceedings of Logic Programming and Nonmonotonic Reasoning Conference, LPNMR 2001. Lecture Notes in Artificial Intelligence, vol. 2.173, pp. 8.1-92. Springer, Berlin Heidelberg New York (2001)
23. Turner, H.: Strong equivalence made easy: Nested expressions and weight constraints. Theory Pract. Log. Program. 3(4&5), 609-622 (2003)
24. van Emden, M.H. Kowalski, R. A.: The semantics of predicate logic as a programming language. J. ACM 23(4), 733-742 (1976)
25. Vennekens, J., Gilis, D., Denecker, M.: Splitting an operator: An algebraic modularity result and its application to auto-epistemic logic. In: Delgrande, J.P., Schaub, T. (eds.) Proceedings of the 10th International Workshop on Non-Monotonic Reasoning, pp. 400-408 (2004)
26. Vennekens, J., Gilis, D., Denecker, M.: Splitting an operator: an algebraic modularity result and its applications to logic programming. In: Lifschitz, V. Demoen, B. (ed.) Logic programming, Proceedings of the 20th International Conference on Logic Programming, ICLP-04, pp. 195-209 (2004)