Propositional theories are strongly equivalent to logic programs

Theory and Practice of Logic Programming

Volumn 7, Issue 6, 2007, Pages 745-759

  Cabalar, Pedro ^a   Ferraris, Paulo ^b  

^a UNIVERSITY OF A CORUÑA   (Spain)

^b University of Texas at Austin   (United States)

Author keywords

Answer sets; Equilibrium logic; Logic of here and there; Strong equivalence

Indexed keywords

MATHEMATICAL MODELS; MATHEMATICAL TRANSFORMATIONS; SEMANTICS; SET THEORY;

ANSWER SETS; EQUILIBRIUM LOGIC; LOGIC OF HERE AND THERE; STRONG EQUIVALENCE;

LOGIC PROGRAMMING;

EID: 35448976068     PISSN: 14710684     EISSN: 14753081     Source Type: Journal    
DOI: 10.1017/S1471068407003110     Document Type: Article

References (17)

1. BIBEL, W. AND EDER, E. 1993. A survey of logical calculi. In The Handbook of Logic in AI and Logic Programming. Vol. 1, Oxford University Press, 67-182.
2. CABALAR, P., PEARCE, D. AND VALVERDE, A. 2005. Reducing propositional theories in equilibrium logic to logic programs. In Proceedings of the 12th Portuguese Conference on Artificial Intelligence (EPIA'05). Lecture Notes in Computer Science, vol. 3808. Springer-Verlag, Berlin, Heidelberg, 4-17.
3. CABALAR, P., PEARCE, D. AND VALVERDE, A. 2006. Minimal logic programs. Unpublished draft.
4. FERRARIS, P. 2005. Answer sets for propositional theories. In Proceedings of the 8th International Conference, on Logic Programming and Nonmonotonic Reasoning. Springer-Verlag, Berlin, Heidelberg, 119-131.
5. FERRARIS, P. AND LIFSCHITZ, V. 2005. Weight constraints as nested expressions. Theory and Practice of Logic Programming 5, 45-74.
6. GELFOND, M. AND LIFSCHITZ, V. 1988. The stable models semantics for logic programming. In Proceedings of the 5th International Conference on Logic Programming. The MIT Press, Cambridge, MA, 1070-1080.
7. GELFOND, M. AND LIFSCHITZ, V. 1991. Classical negation in logic programs and disjunctive databases. New Generation Computing 9, 365-385.
8. HEYTING, A. 1930. Die formalen Regeln der intuitionistischen Logik. Sitzungsberichte der Preussischen Akademie der Wissenschaften, Physikalisch-mathematische Klasse, 42-56.
9. INOUE, K. AND SAKAMA, C. 1998. Negation as failure in the head. Journal of Logic Programming 35(1), 39-78.
10. JONGH, D. D. AND HENDRIKS, L. 2003. Characterization of strongly equivalent logic programs in intermediate logics. TPLP 3(3), 259-270.
11. LIFSCHITZ, V., PEARCE, D. AND VALVERDE, A. 2001. Strongly equivalent logic programs. ACM Transactions on Computational Logic 2, 526-541.
12. LIFSCHITZ, V., TANG, L. R. AND TURNER, H. 1999. Nested expressions in logic programs. Annals of Mathematics and Artificial Intelligence 25, 369-389.
13. LIFSCHITZ, V. AND WOO, T. 1992. Answer sets in general nonmonotonic reasoning (preliminary report). In Proceedings of Third International Conference on Principles of Knowledge Representation and Reasoning, B. Nebel, C. Rich and W. Swartout, Eds. Morgan Kaufmann, San Mateo, CA, 603-614.
14. LUKASIEWICZ, J. 1941, Die logik und das grundlagenproblem. Les Entries de Zürich sur les Fondaments et la Méthode des Sciences Mathématiques 12, 6-9 (1938), 82-100.
15. MCCLUSKEY, E. J. 1956. Minimization of boolean functions. Bell System Technical Journal 35, 1417-1444.
16. PEARCE, D. 1997. A new logical characterisation of stable models and answer sets. In Non monotonie extensions of logic programming. Proceedings of NMELP'96. (LNAI 1216). Springer-Verlag.
17. QUINE, W. V. O. 1952. The problem of simplifying truth functions. American Mathematical Monthly 59, 521-531.