Abstract
The purpose of this work is to clarify the relationship between three approaches to representing incomplete information in logic programming. Classical negation and epistemic disjunction are used in the first of these approaches, abductive logic programs with classical negation in the second, and a simpler form of abductive logic programming — without classical negation — in the third. In the literature, these ideas have been illustrated with examples related to properties of actions, and in this paper we consider an action domain also. We formalize this domain as a disjunctive program with classical negation, and then show how two abductive formalizations can be obtained from that program by a series of simple syntactic transformations. The three approaches under consideration turn out to be parts of a whole spectrum of different, but equivalent, ways of representing incomplete information.
This work was partially supported by the National Science Foundation under grant IRI-9306751. The second author is also supported by an IBM Graduate Fellowship.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
Krzysztof Apt and Marc Bezem. Acyclic programs. In David Warren and Peter Szeredi, editors, Logic Programming: Proc. of the Seventh Int'l Conf., pages 617–633, 1990.
Krzysztof Apt, Howard Blair, and Adrian Walker. Towards a theory of declarative knowledge. In Jack Minker, editor, Foundations of Deductive Databases and Logic Programming, pages 89–148. Morgan Kaufmann, San Mateo, CA, 1988.
Mark Denecker and Danny De Schreye. Representing incomplete knowledge in abductive logic programming. In Dale Miller, editor, Logic Programming: Proceedings of the 1993 Int'l Symposium, pages 147–163, 1993.
Phan Minh Dung. Representing actions in logic programming and its applications in database updates. In Logic Programming: Proceedings of the Tenth Int'l Conf. on Logic Programming, pages 222–238, 1993.
Kave Eshghi and Robert Kowalski. Abduction compared with negation as failure. In Giorgio Levi and Maurizio Martelli, editors, Logic Programming: Proc. of the Sixth Int'l Conf., pages 234–255, 1989.
Chris Evans. Negation-as-failure as an approach to the Hanks and McDermott problem. In Proc. of the Second Int'l Symp. on Artificial Intelligence, 1989.
Michael Gelfond. Epistemic approach to formalization of commonsense reasoning. Technical Report TR-91-2, University of Texas at El Paso, Department of Computer Science, 1991.
Michael Gelfond and Vladimir Lifschitz. Classical negation in logic programs and disjunctive databases. New Generation Computing, 9:365–385, 1991.
Michael Gelfond and Vladimir Lifschitz. Representing action and change by logic programs. The Journal of Logic Programming, 17:301–322, 1993.
Steve Hanks and Drew McDermott. Nonmonotonic logic and temporal projection. Artificial Intelligence, 33(3):379–412, 1987.
Katsumi Inoue and Chiaki Sakama. Transforming abductive logic programs to disjunctive programs. In Logic Programming: Proceedings of the Tenth Int'l Conf. on Logic Programming, pages 335–353, 1993.
Katsumi Inoue and Chiaki Sakama. On positive occurrences of negation as failure. In Proc. of the Fourth Int'l Conf. on Principles of Knowledge Representation and Reasoning, pages 293–304, 1994.
Antonis Kakas and Paolo Mancarella. Generalized stable models: a semantics for abduction. In Proc. of ECAI-90, pages 385–391, 1990.
Vladimir Lifschitz and Hudson Turner. Splitting a logic program. In Logic Programming: Proceedings of the Eleventh Int'l Conf. on Logic Programming, pages 23–37, 1994.
Vladimir Lifschitz and Thomas Woo. Answer sets in general nonmonotonic reasoning (preliminary report). In Bernhard Nebel, Charles Rich, and William Swartout, editors, Proc. of the Third Int'l Conf. on Principles of Knowledge Representation and Reasoning, pages 603–614, 1992.
Teodor Przymusinski. On the declarative semantics of deductive databases and logic programs. In Jack Minker, editor, Foundations of Deductive Databases and Logic Programming, pages 193–216. Morgan Kaufmann, San Mateo, CA, 1988.
Hudson Turner. Signed logic programs. In Logic Programming: Proceedings of the 1994 Int'l Symposium, pages 61–75, 1994.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1995 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Lifschitz, V., Turner, H. (1995). From disjunctive programs to abduction. In: Dix, J., Pereira, L.M., Przymusinski, T.C. (eds) Non-Monotonic Extensions of Logic Programming. NMELP 1994. Lecture Notes in Computer Science, vol 927. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0030658
Download citation
DOI: https://doi.org/10.1007/BFb0030658
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-59467-3
Online ISBN: 978-3-540-49272-6
eBook Packages: Springer Book Archive