Abstract
There are three most prominent semantics defined for certain subclasses of disjunctive logic programs: GCWA (for positive programs), PERFECT (for stratified programs) and STABLE (defined for the whole class of all disjunctive programs). While there are various competitors based on 3-valued models, notably WFS and its disjunctive counterparts, there are no other semantics consisting of 2-valued models. We argue that the reason for this is the Partial Evaluation-property (also called Unfolding or Partial Deduction) wellknown from Logic Programming. In fact, we prove characterizations of these semantics and show that if a semantics SEM satisfies Partial Evaluation and Elimination of Taulologies then (1) SEM is based on 2-volued minimal models for positive programs, and (2) if SEM satisfies in addition Elimination of Contradictions, it is based on stable models. We also show that if we require Isomorphy and Relevance then STABLE is completely determined on the class of all stratified disjunctive logic programs. The underlying notion of a semantics is very general and our abstract properties state that certain syntactical transformations on programs are equivalence preserving.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
K. Apt, H. Blair, and A. Walker. Towards a theory of declarative knowledge. In Jack Minker, editor, Foundations of Deductive. Databases, chapter 2, pages 80–148. Morgan Kaufmann, 1988.
Stefan Brass and Jürgen Dix. A Characterization of the Stable Semantics by Partial Evaluation. In Proc. of the 10th Workshop on Logic Programming, Zuerich, October 1994, 1994.
Stefan Brass and Jürgen Dix. A disjunctive semantics based on unfolding and bottom-up evaluation. In Bernd Wolfinger, editor, Innovationen bei Rechenund Kommunikationssystemen, (IFIP-Congress, Workshop FG2: Disjunctive Logic Programming and Disjunctive Databases), pages 83–91. Springer-Verlag, 1994.
Stefan Brass and Jürgen Dix. A General Approach to Bottom-Up Computation of Disjunctive Semantics. In J. Dix, L. Pereira, and T. Przymusinski, editors, Nonmonotonic Extensions of Logic Programming, pages 127–155. Springer LNCS, to appear, 1995.
Stefan Brass and Jürgen Dix. Disjunctive Semantics based upon Partial and Bottom-Up Evaluation. In Leon Sterling, editor, Proceedings of the 12th Int. Conf. on Logic Programming, Tokyo. MIT, June 1995.
François Bry. Negation in logic programming: A formalization in constructive logic. In Dimitris Karagiannis, editor, Information Systems and Artificial Intelligence: Integration Aspects, pages 30–46. Springer, 1990.
Jürgen Dix. A Framework for Representing and Characterizing Semantics of Logic Programs. In B. Nebel, C. Rich, and W. Swartout, editors, Principles of Knowledge Representation and Reasoning: Proceedings of the Third International Conference (KR '92), pages 591–602. San Mateo, CA, Morgan Kaufmann, 1992.
Jürgen Dix. A Classification-Theory of Semantics of Normal Logic Programs: II. Weak Properties. Fundamenta Informaticae, XXII(3), pages 257–288, 1995.
Jürgen Dix and Martin Müller. An Axiomatic Framework for Representing and Characterizing Semantics of Disjunctive Logic Programs. In Pascal Van Hentenryck, editor, Proceedings of the 11th Int. Conf. on Logic Programming, S. Margherita Ligure, pages 303–322. MIT, June 1994.
Jürgen Dix and Martin Müller. Partial Evaluation and Relevance for Approximations of the Stable Semantics. In Z.W. Ras and M. Zemankova, editors, Proceedings of the 8th Int. Symp. on Methodologies for Intelligent Systems, Charlotte, NC, 1994, pages 511–520. Springer, Lecture Notes in Artificial Intelligence 869, 1994.
P. M. Dung and K. Kanchansut. A fixpoint approach to declarative semantics of logic programs. In E.L. Lusk and R.A. Overbeek, editors, Proceedings of North American Conference Cleveland,Ohio, USA. MIT, October 1989.
Michael Gelfond and Vladimir Lifschitz. Classical Negation in Logic Programs and Disjunctive Databases. New Generation Computing, 9:365–387, 1991.
Yong Hu and Li Yan Yuan. Extended Well-Founded Model Semantics for General Logic Programs. In Koichi Furukawa, editor, Proceedings of the 8th Int. Conf. on Logic Programming, Paris, pages 412–425. MIT, June 1991.
Jack Minker. On indefinite databases and the closed world assumption. In Proceedings of the 6th Conference on Automated Deduction, New York, pages 292–308. Springer, 1982.
Teodor Przymusinski. On the declarative semantics of deductive databases and logic programs. In Jack Minker, editor, Foundations of Deductive Databases, chapter 5, pages 193–216. Morgan Kaufmann, 1988.
Teodor Przymusinski. Stable Semantics for Disjunctive Programs. New Generation Computing Journal, 9:401–424, 1991.
Teodor Przymusinski. Static Semantics For Normal and Disjunctive Logic Programs. Annals of Mathematics and Artificial Intelligence, Special Issue on Disjunctive Programs: to appear, 1995.
Chiaki Sakama and Hirohisa Seki. Partial Deduction of Disjunctive Logic Programs: A Declarative Approach. In Fourth International Workshop on Logic Program Synthesis and Transformation (LOPSTR '94). Lecture Notes in Computer Science, Springer-Verlag, July 1994.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1995 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Brass, S., Dix, J. (1995). Characterizations of the stable semantics by partial evaluation. In: Marek, V.W., Nerode, A., Truszczyński, M. (eds) Logic Programming and Nonmonotonic Reasoning. LPNMR 1995. Lecture Notes in Computer Science, vol 928. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-59487-6_7
Download citation
DOI: https://doi.org/10.1007/3-540-59487-6_7
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-59487-1
Online ISBN: 978-3-540-49282-5
eBook Packages: Springer Book Archive