Skip to main content
SpringerLink
Log in

A Nonmonotonic Extension to Horn-Clause Logic

  • Chapter
Automated Practical Reasoning

Part of the book series: Texts and Monographs in Symbolic Computation ((TEXTSMONOGR))

  • 95 Accesses

Abstract

Standard first-order logic, and therefore, any description of the world that relies on it, ordinarily requires the absence of contradiction. It has been repeatedly pointed out that in describing the real world it is often very difficult to avoid making contradictory statements (e.g., when realizing that an assumption had proven wrong, we might have to assert the denial of what we had assumed to hold true). The example that has become a classic in the AI literature is the problem that Birds fly, Penguins are birds, but Penguins don’t fly.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 74.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Apt, K. R., Blair, H. A., Walker, A. (1988): Towards a theory of declarative knowledge. In: Minker, J. (ed.): Foundations of deductive databases and logic programming. Morgan Kaufmann, Los Altos, pp. 89–148.

    Google Scholar 

  • Apt, K. R., van Emden, M. H. (1982): Contributions to the theory of logic programming. J. ACM 29: 841–862.

    Article  MATH  Google Scholar 

  • Blair, H. A. (1986): Decidability in the Herbrand base. In: Minker, J. (ed.): Proceedings Foundations of Deductive Databases and Logic Programming, Washington, 1986.

    Google Scholar 

  • Chang, C., Lee, R. (1973): Symbolic logic and mechanical theorem proving. Academic Press, New York.

    MATH  Google Scholar 

  • Clark, K. L. (1978): Negation as failure. In: Gallaire, H., Minker, J. (eds.): Logic and databases. Plenum, New York, pp. 293–322.

    Google Scholar 

  • Gallaire, H., Minker, J. (eds.) (1978): Logic and databases. Plenum, New York.

    Google Scholar 

  • Gelfond, M., Lifschitz, V. (1988): The stable model semantics for logic programming. In: Proceedings of the 5th International Conference on Logic Programming, Seattle, 1988, pp. 1070–1081.

    Google Scholar 

  • Gelfond, M., Lifschitz, V. (1989): Compiling circumscriptive theories into logic programs. In: Reinfrank, M., de Kleer, J., Ginsberg, M. L., Sandewall, E. (eds.): Nonmonotonic reasoning. Springer, Berlin Heidelberg New York Tokyo, pp. 74–99 (Lecture notes in computer science, vol. 346).

    Google Scholar 

  • Genesereth, M., Nilsson, N. (1988): Logical foundations of artificial intelligence. Morgan Kaufmann, Los Altos.

    Google Scholar 

  • Ginsberg, M. L. (ed.) (1987): Readings in nonmonotonic reasoning. Morgan Kaufmann, Los Altos.

    Google Scholar 

  • Jaffar, J., Stuckley, P. J. (1986): Canonical logic programs. J. Logic Program. 3: 143–157.

    Article  MATH  Google Scholar 

  • Lifschitz, V. (1985): Closed world databases and circumscription. Artif. Intell. 27: 229–235.

    Article  MathSciNet  MATH  Google Scholar 

  • Lifschitz, V. (1987): Pointwise circumscription. In: Ginsberg, M. L. (ed.): Readings in nonmonotonic reasoning. Morgan Kaufmann, Los Altos, pp. 179–194.

    Google Scholar 

  • Lloyd, J. W. (1987): Foundations of logic programming. Springer, Berlin Heidelberg New York Tokyo.

    Book  MATH  Google Scholar 

  • McCarthy, J. (1980): Circumscription — a form of nonmonotonic reasoning. Artif. Intell. 13: 27–39.

    Article  MATH  Google Scholar 

  • McDermott, D. (1982): Nonmonotonic logic II. J. ACM 29: 33–57.

    Article  MathSciNet  MATH  Google Scholar 

  • McDermott, D., Doyle, J. (1980): Nonmonotonic logic I. Artif. Intell. 13: 27–39.

    Article  MathSciNet  Google Scholar 

  • Minker, J. (ed.) (1988): Foundations of deductive databases and logic programming. Morgan Kaufmann, Los Altos.

    Google Scholar 

  • Moore, R. (1985): Semantical considerations on nonmonotonic logic. Artif. Intell. 25: 75–94.

    Article  MATH  Google Scholar 

  • Przymusinski, T. (1988): On the semantics of stratified deductive databases. In: Minker, J. (ed.): Foundations of deductive databases and logic programming. Morgan Kaufmann, Los Altos, pp. 193–216.

    Google Scholar 

  • Przymusinski, T. (1989): Nonmonotonic formalisms and logic programming. In: Proceedings of the 6th International Conference on Logic Programming, Pisa, 1989, pp. 655–674.

    Google Scholar 

  • Przymusinski, T. (1991): Well-founded completions of logic programs. In: Proceedings of the 8th International Conference on Logic Programming, Paris, 1991, pp. 726–741.

    Google Scholar 

  • Reinfrank, M., de Kleer, J., Ginsberg, M. L., Sandewall, E. (eds.) (1989): Non-monotonic reasoning. Springer, Berlin Heidelberg New York Tokyo (Lecture notes in computer science, vol. 346).

    Google Scholar 

  • Reiter, R. (1978): On closed world data bases. In: Gallaire, H., Minker, J. (eds.): Logic and databases. Plenum, New York, pp. 55–76.

    Google Scholar 

  • Reiter, R. (1980): A logic for default reasoning. Artif. Intell. 13: 81–132.

    Article  MathSciNet  MATH  Google Scholar 

  • Sheperdson, J. C. (1984): Negation as failure: a comparison of Clark’s completed database and Reiter’s closed world assumption. J. Logic Program. 1: 51–79.

    Article  Google Scholar 

  • Sheperdson, J. C. (1988): Negation in logic programming. In: Minker, J. (ed.): Foundations of deductive databases and logic programming. Morgan Kaufmann, Los Altos, pp. 19–89.

    Google Scholar 

  • Sheperdson, J. C. (1989): Logics for negation as failure. In: Moschovakis, Y. N. (ed.): Logic from computer science. Springer, Berlin Heidelberg New York Tokyo, pp. 521–585 (Mathematical Sciences Research Institute publications, vol. 21).

    Google Scholar 

  • Tarski, A. (1955): A lattice-theoretical fixpoint theorem and its applications. Pacific J. Math. 5: 285–309.

    MathSciNet  MATH  Google Scholar 

  • Tsai, J. P., Weigert, T. (1989): Exploratory prototyping through the use of frame and production systems. In: Proceedings IEEE Computer Software and Applications Conference, Orlando, 1989, pp. 445–462.

    Google Scholar 

  • Tsai, J. P., Weigert, T. (1990): A knowledge-based approach for checking software information using a non-monotonic reasoning system. Knowl. Based Syst. 3: 131–138.

    Article  Google Scholar 

  • Tsai, J. P., Weigert, T. (1991): HCLIE: a logic-based requirements language for new software engineering paradigms. IEE Software Eng. J. 6: 137–151.

    Article  Google Scholar 

  • Tsai, J. P., Weigert, T. (1992): An explication of reasoning in multiple inheritance system through non-monotonic Horn clause logic. J. Inf. Sci. 63: 261–283.

    Article  MathSciNet  MATH  Google Scholar 

  • Tsai, J. P., Weigert, T. (1993): Knowledge-based software development for real-time distributed systems. World Scientific Publishing, Singapore.

    Book  MATH  Google Scholar 

  • Tsai, J. P., Weigert, T., Aoyama, M. (1988): A declarative approach to software requirements specification language. In: Proceedings IEEE Computer Languages Conference, Miami Beach, 1988, pp. 414–421.

    Google Scholar 

  • Tsai, J. P., Weigert, T., Jang, H. C. (1990): A hybrid knowledge representation as a basis of requirement specification and reasoning. In: Proceedings IEEE Computer Software and Applications Conference, Chicago, 1990, pp. 70–76.

    Google Scholar 

  • Tsai, J. P., Weigert, T., Jang, H. C. (1991): Non-monotonic logic as a basis for requirements specification and analysis. In: Proceedings of the International Symposium on Artificial Intelligence, Tokyo, 1991, pp. 13–15.

    Google Scholar 

  • Tsai, J. P., Weigert, T., Jang, H. C. (1992): A hybrid knowledge representation as a basis of requirement specification and specification analysis. IEEE Trans. Software Eng. 18: 1076–1100.

    Article  Google Scholar 

  • van Gelder, A., Ross, K., Schlipf (1988): Unfounded sets and well-founded semantics for general logic programs. In: Proceedings of the Symposium on Principles of Database Systems. ACM SIGACT-SIGMOD.

    Google Scholar 

  • Weigert, T. (1989): Nonmonotonic logic as the basis for a requirement specification language. In: Lowry, M. (ed.): Proceedings of the Workshop on Automating Software Design, St. Paul, 1989, pp. 191–206.

    Google Scholar 

  • Weigert, T., Tsai, J. P. (1994): A computationally tractable nonmonotonic logic. IEEE Trans. Knowl. Data Eng. 6: 57–64.

    Article  Google Scholar 

Download references

Authors
  1. Thomas J. Weigert
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Research Institute for Symbolic Computation, Johannes-Kepler-University Linz, Linz, Austria

    Jochen Pfalzgraf

  2. Laboratoire d’Informatique Fondamentale et d’Intelligence Artificielle, Institut National Polytechnique de Grenoble, Grenoble, France

    Dongming Wang

Rights and permissions

Reprints and permissions

Copyright information

© 1995 Springer-Verlag Wien

About this chapter

Cite this chapter

Weigert, T.J. (1995). A Nonmonotonic Extension to Horn-Clause Logic. In: Pfalzgraf, J., Wang, D. (eds) Automated Practical Reasoning. Texts and Monographs in Symbolic Computation. Springer, Vienna. https://doi.org/10.1007/978-3-7091-6604-8_10

Download citation

  • DOI: https://doi.org/10.1007/978-3-7091-6604-8_10

  • Publisher Name: Springer, Vienna

  • Print ISBN: 978-3-211-82600-3

  • Online ISBN: 978-3-7091-6604-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation