Abstract
We provide a nine-valued logic to characterize the models of logic programs under a paraconsistent well-founded semantics with explicit negation WFSX p. We define a truth-functional logic, \(\mathcal{N}\mathcal{I}\mathcal{N}\mathcal{E}\), based on the bilattice construction of Ginsberg and Fitting. The models identified by WFSX p are models of logic \(\mathcal{N}\mathcal{I}\mathcal{N}\mathcal{E}\). We conclude with a discussion on the conditions to obtain an isomorphism between the two definitions, and thereby characterizing WFSXp model-theoretically.
We thank Esprit BR project Compulog 2 (no. 6810), and JNICT for their support.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
J. J. Alferes, C. V. Damásio, and L. M. Pereira. A logic programming system for non-monotonic reasoning. Journal of Automated Reasoning, Special Issue on Implementation of NonMonotonic Reasoning(14):93–147,1995.
J. J. Alferes and L. M. Pereira. Reasoning with Logic Programming. Springer-Verlag, 1995. In print.
N. D. Belnap. A useful four-valued logic. In G. Epstein and J. M. Dunn, editors, Modern Uses of Many-valued Logic, pages 8–37. Reidel, 1977.
H. A. Blair and V. S. Subrahmanian. Paraconsistent logic programming. Theoretical Computer Science, 68:135–154, 1989.
S. Brass and J. Dix. A disjunctive semantics based on unfolding and bottom-up evaluation. In Proc. IFIP '94-Congress, Workshop FG2: Disjunctive Logic Programming and Disjunctive Databases, pages 83–91. Springer, 1994.
M. Fitting. Bilattices and the semantics of logic programming. Journal of Logic Programming, 11:91–116,1991.
A. V. Gelder, K. A. Ross, and J. S. Schlipf. The well-founded semantics for general logic programs. Journal of the ACM, 38(3):620–650, 1991.
M. Gelfond and V. Lifschitz. Logic programs with classical negation. In Warren and Szeredi, editors, 7th ICLP, pages 579–597. MIT Press, 1990.
M. L. Ginsberg. Multivalued logics: a uniform approach to reasoning in artificial intelligence. Computational Intelligence, 4:265–316, 1988.
C. M. Jonker and C. Witteveen. Revision by expansion. In G. Lakemeyer and B. Nebel, editors, Proceedings ECAI'92 Workshop on Theoretical Foundations of Knowledge Representation, pages 40–44. ECAI'92 Press, 1992.
R. Kowalski and F. Sadri. Logic programs with exceptions. In Warren and Szeredi, editors, 7th ICLP. MIT Press, 1990.
D. Pearce and G. Wagner. Reasoning with negative information I: Strong negation in logic programs. In Language, Knowledge and Intentionality, pages 430–453. Acta Philosophica Fennica 49, 1990.
L. M. Pereira and J. J. Alferes. Well founded semantics for logic programs with explicit negation. In B. Neumann, editor, Proc. ECAI, pages 102–106. John Wiley & Sons, 1992.
L. M. Pereira, J. J. Alferes, and J. N. Aparício. Contradiction Removal within Well Founded Semantics. In A. Nerode, W. Marek, and V. S. Subrahmanian, editors, LPNMR'91, pages 105–119. MIT Press, 1991.
L. M. Pereira, J. J. Alferes, and J. N. Aparício. Contradiction removal semantics with explicit negation. In M. Masuch and L. Pólos, editors, Knowledge Representation and Reasoning Under Uncertainty, volume 808 of LNAI, pages 91–106. Springer-Verlag, 1994.
L. M. Pereira, J. N. Aparício, and J. J. Alferes. Non-monotonic reasoning with logic programming. Journal of Logic Programming. Special issue on Nonmonotonic reasoning, 17(2, 3 & 4):227–263,1993.
S. G. Pimentel and W. L. Rodi. Belief revision and paraconsistency in a logic programming framework. In A. Nerode, W. Marek, and V. S. Subrahmanian, editors, LPNMR'91, pages 228–242. MIT Press, 1991.
T. Przymusinski. Extended stable semantics for normal and disjunctive programs. In Warren and Szeredi, editors, 7th ICLP, pages 459–477. MIT Press, 1990.
C. Sakama. Extended well-founded semantics for paraconsistent logic programs. In Fifth Generation Computer Systems, pages 592–599. ICOT, 1992.
C. Sakama and K. Inoue. Paraconsistent stable semantics for extended disjunctive programs. Journal of Logic and Computation, 5(3), 1995.
G. Wagner. A database needs two kinds of negation. In B. Thalheim, J. Demetrovics, and H.-D. Gerhardt, editors, Mathematical Foundations of Database Systems, pages 357–371. LNCS 495, Springer-Verlag, 1991.
G. Wagner. Vivid logic: Knowledge-based reasoning with two kinds of negation. LNAI, 764, 1994.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1995 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Damásio, C.V., Pereira, L.M. (1995). A model theory for paraconsistent logic programming. In: Pinto-Ferreira, C., Mamede, N.J. (eds) Progress in Artificial Intelligence. EPIA 1995. Lecture Notes in Computer Science, vol 990. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60428-6_32
Download citation
DOI: https://doi.org/10.1007/3-540-60428-6_32
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-60428-0
Online ISBN: 978-3-540-45595-0
eBook Packages: Springer Book Archive