Stable Models and an Alternative Logic Programming Paradigm

  • Victor W. Marek
  • Miroslaw Truszczyński
Chapter
Part of the Artificial Intelligence book series (AI)

Summary

In this paper we reexamine the place and role of stable model semantics in logic programming and contrast it with a least Herbrand model approach to Horn programs. We demonstrate that inherent features of stable model semantics naturally lead to a logic programming system that offers an interesting alternative to more traditional logic programming styles of Horn logic programming, stratified logic programming and logic programming with well-founded semantics. The proposed approach is based on the interpretation of program clauses as constraints. In this setting, a program does not describe a single intended model, but a family of its stable models. These stable models encode solutions to the constraint satisfaction problem described by the program. Our approach imposes restrictions on the syntax of logic programs. In particular, function symbols are eliminated from the language. We argue that the resulting logic programming system is well-attuned to problems in the class NP, has a well-defined domain of applications, and an emerging methodology of programming. We point out that what makes the whole approach viable is recent progress in implementations of algorithms to compute stable models of propositional logic programs.

Keywords

Logic Program Logic Programming Stable Model Function Symbol Constraint Satisfaction Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, log in to check access.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [ADP95]
    J.J. Alferes, C.V. Damásio and L.M. Pereira. A logic programming system for nonmonotonic reasoning. Journal of Automated Reasoning, 14:93–147, 1995 MathSciNetMATHCrossRefGoogle Scholar
  2. [AB90]
    K. Apt and H.A. Blair. Arithmetical classification of perfect models of stratified programs. Fundamenta Informaticae, 12:1–17, 1990 MathSciNetGoogle Scholar
  3. [ABW88]
    K. Apt, H.A. Blair, and A. Walker. Towards a theory of declarative knowledge. In J. Minker, editor, Foundations of deductive databases and logic programming, pages 89–142, Los Altos, CA, 1988. Morgan Kaufmann Google Scholar
  4. [ACY91]
    F. Afrati, S. Cosmodakis, and M. Yannakakis. On DATALOG vs. polynomial time. In Proceedings of PODS’91, pages 13–25, 1991 Google Scholar
  5. [ADN97]
    C. Aravindan, J. Dix, and I. Niemelä. Dislop: Toward a disjunctive logic programming system. In Proceedings of the 4th International Conference on Logic Programming and Nonmonotonic Reasoning, pages 341–352, 1997. Springer LN in Computer Science 1265 Google Scholar
  6. [AHV95]
    S. Abiteboul, R. Hull, and V. Vianu. Foundations of Databases. Addison-Wesley Publishing Company, 1995MATHGoogle Scholar
  7. [AN78]
    H. Andreka and I. Nemeti. The generalized completeness of Horn predicate logic as a programming language. Acta Cybernetica, 4:3–10, 1978. MathSciNetMATHGoogle Scholar
  8. [AvE82]
    K.R. Apt and M.H. van Emden. Contributions to the theory of logic programming. Journal of the ACM, 29:841–862, 1982 MATHCrossRefGoogle Scholar
  9. [BF91]
    N.Bidoit and C. Froidevaux. Negation by default and unstratifiable logic programs. Theoretical Computer Science, 78:85–112, 1991MathSciNetMATHCrossRefGoogle Scholar
  10. [BMS95]
    H.A. Blair, W. Marek, and J. Schlipf. The expressiveness of locally stratified programs. Annals of Mathematics and Artificial Intelligence, 15:209–229, 1995 MathSciNetMATHCrossRefGoogle Scholar
  11. [Cho96]
    P. Cholewinski. Automated reasoning with Default Logic. PhD thesis, University of Kentucky, 1996. Ph.D. Thesis.Google Scholar
  12. [CKPR73]
    A. Colmerauer, H. Kanoui, R. Pasero, and P. Roussel. Un système de communication homme-machine en frangais. Technical report, University of Marseille, 1973. Google Scholar
  13. [CL-73]
    C.-L. Chang and C.-T. Lee. Symbolic Logic and Mechanical Theorem Proving. Academic Press, 1973MATHGoogle Scholar
  14. [Cla78]
    K.L. Clark. Negation as failure. In H. Gallaire and J. Minker, editors, Logic and data bases, pages 293–322. Plenum Press, 1978Google Scholar
  15. [CMMT95]
    P. Cholewiński, W. Marek, A. Mikitiuk, and M. Truszczyński. Experimenting with nonmonotonic reasoning. In Proceedings of the 12th International Conference on Logic Programming, pages 267–281. MIT Press, 1995Google Scholar
  16. [CMMT98]
    P. Cholewiński, W. Marek, A. Mikitiuk, and M. Truszczyński. Programming with default logic. Submitted for publication, 1998Google Scholar
  17. [CMMT96]
    P. Cholewiński, W. Marek, and M. Truszczyński. Default reasoning system DeReS. In Proceedings of KR-96, pages 518–528. Morgan Kaufmann, 1996 Google Scholar
  18. [CP98]
    M. Cadoli and L. Palipoli. Circumscribing datalog: expressive power and complexity. Theoretical Computer Science, 193:215–244, 1998MathSciNetMATHCrossRefGoogle Scholar
  19. [CPSV98]
    M. Cadoli, L. Palipoli, A. Schaerf, and D. Vasile. Np-spec: An executable specification language for solving all problems in np. Unpublished manuscript, 1998. Google Scholar
  20. [DABC96]
    O. Dubois, P. Andre, Y. Boufkhad, and J. Carlier. Sat versus unsat. In Cliques, Coloring and Satisfiability, Second DIM ACS Implementation Challenge, pages 415–436. American Mathematical Society, 1996Google Scholar
  21. [ELM+97]
    T. Eiter, N. Leone, C. Mateis, G. Pfeifer, and F. Scarcello. A deductive system for non-monotonic reasoning. In Proceedings of the 4th International Conference on Logic Programming and Nonmonotonic Reasoning, pages 363–374, 1997. Springer LN in Computer Science 1265Google Scholar
  22. [ELM+98]
    T. Eiter, N. Leone, C. Mateis, G. Pfeifer, and F. Scarcello. The KR System dlv: Progress Report, Comparisons, and Benchmarks. In Proceedings Sixth International Conference on Principles of Knowledge Representation and Reasoning (KR-98), pages 406–417, June 2–4 1998 Google Scholar
  23. [GJ79]
    M.R. Garey and D.S. Johnson. Computers and intractability; a guide to the theory of NP-completeness. W.H. Freeman, 1979MATHGoogle Scholar
  24. [GL88]
    M. Gelfond and V. Lifschitz. The stable semantics for logic programs. In Proceedings of the 5th International Symposium on Logic Programming, pages 1070–1080, Cambridge, MA, 1988. MIT Press Google Scholar
  25. [Her30]
    J. Herbrand. Recherches sur la théorie de la démonstrations. PhD thesis, Paris, 1930Google Scholar
  26. [Kam97]
    M. Kaminski. A note on stable semantics for logic programs. Artificial Intelligence Journal, 96:467–479, 1997.MathSciNetMATHCrossRefGoogle Scholar
  27. [Kow74]
    R. Kowalski. Predicate logic as a programming language. In Proceedings of IFIP 74, pages 569–574, Amsterdam, 1974. North HollandGoogle Scholar
  28. [Kow79]
    R. Kowalski. Logic for Problem Solving. North Holland, Amsterdam, 1979.MATHGoogle Scholar
  29. [Lif98]
    V. Lifschitz. Action languages, answer sets and planning. This volume.Google Scholar
  30. [Llo84]
    J. Lloyd. Foundations of logic programming. Berlin: Springer-Verlag, 1984.MATHGoogle Scholar
  31. [Lov78]
    D. Loveland. Automated Theorem Proving: A Logical Basis. North Holland, 1978. MATHGoogle Scholar
  32. [LT84]
    J.W. Lloyd and R.W. Topor. Making prolog more expressive. Journal of Logic Programming, l (3):225–240, 1984 MathSciNetCrossRefGoogle Scholar
  33. [MNR94]
    W. Marek, A. Nerode, and J. B. Remmel. The stable models of predicate logic programs. Journal of Logic Programming, 21(3):129–154, 1994 MathSciNetGoogle Scholar
  34. [MT89]
    W. Marek and M. Truszczyński. Stable semantics for logic programs and default theories. In Proceedings of the North American Conference on Logic Programming, pages 243–256. MIT Press, 1989 Google Scholar
  35. [MT91]
    W. Marek and M. Truszczyński. Autoepistemic logic. Journal of the ACM, 38:588–619, 1991 MATHCrossRefGoogle Scholar
  36. [MT93]
    W. Marek and M. Truszczyński. Nonmonotonic Logic - Context- Dependent Reasoning. Series Artificial Intelligence, Springer-Verlag, 1993Google Scholar
  37. [MW88]
    D. Maier and D. S. Warren. Computing with logic. Logic programming with Prolog. The Benjamin/Cummings Publishing Company, Inc., 1988 MATHGoogle Scholar
  38. [Nie98]
    I. Niemelä. Logic programs with stable model semantics as a constraint programming paradigm. In Proceedings of the Workshop on Computational Aspects of Nonmonotonic Reasoning, pages 72–79, 1998Google Scholar
  39. [NS95]
    I. Niemelä and P. Simons. Evaluating an algorithm for default reasoning. In Proceedings of the IJCAI-95 Workshop on Applications and Implementations of Nonmonotonic Reasoning Systems, 1995 Google Scholar
  40. [NS96]
    I. Niemelä and P. Simons. Efficient implementation of the well-founded and stable model semantics. In Proceedings of JICSLP-96. MIT Press, 1996 Google Scholar
  41. [Prz88]
    T. Przymusiński. On the declarative semantics of deductive databases and logic programs. In Foundations of deductive databases and logic programming, pages 193–216, Los Altos, CA, 1988. Morgan Kaufmann Google Scholar
  42. [Prz90]
    T. Przymusiński. The Well-Founded Semantics Coincides With The Three-Valued Stable Semantics, Fundamenta Informaticae, 13:445–464, 1990.MathSciNetMATHGoogle Scholar
  43. [Rei80]
    R. Reiter. A logic for default reasoning. Artificial Intelligence, 13:81–132, 1980.MathSciNetMATHCrossRefGoogle Scholar
  44. [Rob65]
    J.A. Robinson. Machine-oriented logic based on resolution principle. Journal of the ACM, 12:23–41, 1965.MATHCrossRefGoogle Scholar
  45. [RRS+97]
    P. Rao, I.V. Ramskrishnan, K. Sagonas, T. Swift, D. S. Warren, and J. Freire. XSB: A system for efficiently computing well-founded semantics. In Proceedings of LPNMR ’97, pages 430–440, Lecture Notes in Computer Science, 1265, Springer-Verlag, 1997Google Scholar
  46. [Sch95]
    J. Schlipf. The expressive powers of the logic programming semantics. Journal of the Computer Systems and Science, 51:64–86, 1995.MathSciNetMATHCrossRefGoogle Scholar
  47. [SK92]
    B. Selman and H. A. Kautz. Planning as satisfiability. In Proceedings of the 10th European Conference on Artificial Intelligence, Vienna, Austria, 1992 Google Scholar
  48. [SK93]
    B. Selman and H. Kautz. Domain-independent extensions to GSAT: Solving large structured satisfiability problems. In Proceedings of IJCAI-93, San Mateo, CA, Morgan Kaufmann, 1993 Google Scholar
  49. [SKC94]
    B. Selman, H.A. Kautz, and B. Cohen. Noise strategies for improving local search. In Proceedings of the Twelfth National Conference on Artificial Intelligence (AAAI-94), Seattle, USA, AAAI Press, 1994. Google Scholar
  50. [Smu68]
    R.M. Smullyan. First-Order Logic. Springer-Verlag, 1968 MATHGoogle Scholar
  51. [U1188]
    J.D. Ullman. Principles of Database and Knowledge-Base Systems. Computer Science Press, Rockville, MD, 1988 Google Scholar
  52. [VRS91]
    A. Van Gelder, K.A. Ross, and J.S. Schlipf. Unfounded sets and well- founded semantics for general logic programs. Journal of the ACM, 38:620–650, 1991 MATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Victor W. Marek
    • 1
  • Miroslaw Truszczyński
    • 1
  1. 1.Department of Computer ScienceUniversity of KentuckyLexingtonUSA

Personalised recommendations