Abstract
Limiting the number of times a variable appears in either the head or the body of a rule, we identify two classes of normal prepositional logic programs. These classes have the desirable property that stable models, if they exist, can be found in linear time (worst case). We also identify a related class containing programs for which the well-founded model can be acquired in linear time, yet for which computing the stable model(s) remains NP-complete. We show in this class how, by relaxing one constraint, previously linear complexity is increased to intractability.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
Rachel Ben-Eliyahu. A hierarchy of tractable subsets for computing stable models. Journal of Artificial Intelligence Research, 5:27–52, 1996.
Corman, Leiserson, and Rivest. Introduction to Algorithms. McGraw-Hill, 1991.
Yannis Dimopoulos. On computing logic programs. In Proceedings of Applications and Implementations of Nonmonotonic Reasoning Systems, 1996.
Yannis Dimopoulos and Alberto Torres. Graph theoretical structures in logic programs and default theories. Technical report, Max-Planck-Institut Fur Informatik, Im Stadtwalk, 66123 Saarbrucken, Germany, 1993.
C. Elkan. A rational reconstruction of nonmonotonic truth maintenance systems. Artificial Intelligence, 43:219–234, 1990.
Melvin Fitting. A kripke-kleene semantics for logic programs. Journal of Logic Programming, 2(4):295–312, 1985.
Michael R. Garey and David S. Jonson. Computers and Intractability: A Guide to the Theory of NP-Completeness. W.H.Freeman and company, 1979.
A. Van Gelder, K. Ross, and J. Schlipf. The well-founded semantics for general logic programs. Journal of the ACM, 38(3), July 1991.
Michael Gelfond and Vladimir Lifschitz. The stable model semantics for logic programming. In Proceedings of the Fifth Logic Programming Symposium, 1990.
H. Blair K. R. Apt and A. Walker. Towards a theory of declarative knowledge. Foundations of Deductive Databases and Logic Programming, pages 89–148, 1988.
J. W. Lloyd. Foundations of Logic Programming. Springer-Verlag, 1984.
A. Marek and M. Truszczynski. Autoepistemic logic. Technical report, University of Kentucky, University of Kentucky, Lexington, KY, 1988.
A. Wiktor Marek and Miroslaw Truszczynski. Autoepistemic logic. Journal of the ACM, 38(3), July 1991.
T. C. Przymusinski. Every logic program has a natural stratification and and iterated fixed point model. In Proceedings of the Eighth ACM Symposium on Principles of Database Systems, pages 11–21, 1989.
John Schlipf. The expressive powers of the logic programming semantics. In Ninth ACM Symposium on Principles of Database Systems, 1990.
John Schlipf. Logic Programming Semantics, chapter A Comparison of Notions of Negation as Failure. Oxford University Press, 1994.
Jennifer Seitzer. Doctoral proposal: A study of the well-founded and stable logic programming semantics. 1996.
V. S.Subrahmanian. Personal communication.
R. Tarjan. Depth first search and linear graph algorithms. SIAM Journal on Computing, 1:146–160, 1972.
Jeffrey D. Ullman. Principles of Database and Knowledge-Base Systems, Vol I. Computer Science Press, Inc., 1988.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1997 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Seitzer, J., Schlipf, J. (1997). Affordable classes of normal logic programs. In: Dix, J., Furbach, U., Nerode, A. (eds) Logic Programming And Nonmonotonic Reasoning. LPNMR 1997. Lecture Notes in Computer Science, vol 1265. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-63255-7_7
Download citation
DOI: https://doi.org/10.1007/3-540-63255-7_7
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-63255-9
Online ISBN: 978-3-540-69249-2
eBook Packages: Springer Book Archive