Skip to main content

Knowledge representation with logic programs

  • Introduction
  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 1471))

Abstract

In this overview we show how Knowledge Representation (KR) can be done with the help of generalized logic programs. We start by introducing the core of PROLOG, which is based on definite logic programs. Although this class is very restricted (and will be enriched by various additional features in the rest of the paper), it has a very nice property for KR-tasks: there exist efficient Query-answering procedures — a Top-Down approach and a Bottom-Up evaluation. In addition we can not only handle ground queries but also queries with variables and compute answer-substitutions.

It turns out that more advanced KR-tasks can not be properly handled with definite programs. Therefore we extend this basic class of programs by additional features like Negation-as-Finite-Failure, Default-Negation, Explicit Negation, Preferences, and Disjunction. The need for these extensions is motivated by suitable examples and the corresponding semantics are discussed in detail.

Clearly, the more expressive the respective class of programs under a certain semantics is, the less efficient are potential Query-answering methods. This point will be illustrated and discussed for every extension. By well-known recursion-theoretic results, it is obvious that there do not exist complete Query-answering procedures for the general case where variables and function symbols are allowed. Nevertheless we consider it an important topic of further research to extract feasible classes of programs where answer-substitutions can be computed.

This is a short version of Chapter 6 in D. Gabbay and F. Guenthner (editors), Handbook of Philosophical Logic, 2nd Edition, Volume 6, Methodologies, Reidel Publ., 1999

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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. J. J. Alferes, Carlos Viegas Damasio, and L. M. Pereira. A logic programming system for non-monotonic reasoning. Journal of Automated Reasoning, 14(1):93–147, 1995.

    Article  MATH  MathSciNet  Google Scholar 

  2. Jose Julio Alferes and Luiz Moniz Pereira. An argumentation theoretic semantics based on non-refutable falsity. In J. Dix, L. Pereira, and T. Przymusinski, editors, Nonmonotonic Extensions of Logic Programming, LNAI 927, pages 3–22. Springer, Berlin, 1995.

    Google Scholar 

  3. Jose Julio Alferes and Luiz Moniz Pereira, editors. Reasoning with Logic Programming, LNAI 1111, Berlin, 1996. Springer.

    Google Scholar 

  4. Jose Julio Alferes, Luiz Moniz Pereira, and Teodor Przymusinski. Strong and Explicit Negation in Non-Monotonic Reasoning and Logic Programming. In J.J Alferes, L.M. Pereira, and E. Orlowska, editors, Logics in Artificial Intelligence (JELIA '96), LNCS 1126, pages 143–163. Springer, 1996.

    Google Scholar 

  5. Krzysztof R. Apt. Logic programming. In J. van Leeuwen, editor, Handbook of Theoretical Computer Science, Vol. B, chapter 10, pages 493–574. Elsevier Science Publishers, 1990.

    Google Scholar 

  6. Krzysztof R. Apt and Roland N. Bol. Logic Programming and Negation: A Survey. Journal of Logic Programming, 19–20:9–71, 1994.

    Article  MathSciNet  Google Scholar 

  7. Chandrabose Aravindan. An abductive framework for negation in disjunctive logic programming. In J. J. Alferes, L. M. Pereira, and E. Orlowska, editors, Proceedings of Joint European workshop on Logics in AI, number 1126 in Lecture Notes in Artificial Intelligence, pages 252–267. Springer-Verlag, 1996. A related report is available on the web from 〈http://www.uni-koblenz.de/~arvind/papers/〉.

    Google Scholar 

  8. Chandrabose Aravindan, Jürgen Dix, and Ilkka NiemelÄ. Dislop: A research project on disjunctive logic programming. AI Communications, 10(3/4):151–165, 1997.

    Google Scholar 

  9. Chandrabose Aravindan, Jürgen Dix, and Ilkka NiemelÄ. DisLoP: Towards a Disjunctive Logic Programming System. In J. Dix, U. Furbach, and A. Nerode, editors, Logic Programming and Non-Monotonic Reasoning, Proceedings of the Fourth International Conference, LNAI 1265, pages 342–353, Berlin, June 1997. Springer.

    Google Scholar 

  10. Chitta Baral and Michael Gelfond. Logic Programming and Knowlege Representation. Journal of Logic Programming, 19–20:73–148, 1994.

    Article  MathSciNet  Google Scholar 

  11. Chitta Baral and V.S. Subrahmanian. Dualities between Alternative Semantics for Logic Programming and Non-monotonic Reasoning. In Anil Nerode, Wiktor Marek, and V. S. Subrahmanian, editors, Logic Programming and Non-Monotonic Reasoning, Proceedings of the first International Workshop, pages 69–86, Cambridge, Mass., July 1991. Washington D.C, MIT Press.

    Google Scholar 

  12. Chitta Baral and V.S. Subrahmanian. Stable and Extension Class Theory for Logic Programs and Default Logics. Journal of Automated Reasoning, 8, No. 3:345–366, 1992.

    Article  MATH  MathSciNet  Google Scholar 

  13. P. Baumgartner and U. Furbach. Model Elimination without Contrapositives and its Application to PTTP. Journal of Automated Reasoning, 13:339–359, 1994. Short version in: Proceedings of CADE-12, Springer LNAI 814, 1994, pp 87–101.

    Article  MathSciNet  Google Scholar 

  14. P. Baumgartner, U. Furbach, and I. NiemelÄ. Hyper Tableaux. In Proc. JELIA 96, number 1126 in LNAI. European Workshop on Logic in AI, Springer, 1996. (Long version in: Fachberichte Informatik, 8–96, UniversitÄt Koblenz-Landau).

    Google Scholar 

  15. P. Baumgartner, U. Furbach, and F. Stolzenburg. Model Elimination, Logic Programming and Computing Answers. In Proceedings of IJCAI '95, 1995. (to appear, Long version in: Research Report 1/95, University of Koblenz, Germany).

    Google Scholar 

  16. Catril Beeri and Raghu Ramakrishnan. On the power of magic. The Journal of Logic Programming, 10:255–299, 1991.

    Article  MATH  MathSciNet  Google Scholar 

  17. Colin Bell, Anil Nerode, Raymond T. Ng, and V. S. Subrahmanian. Implementing Stable Semantics by Linear Programming. In Luis Moniz Pereira and Anil Nerode, editors, Logic Programming and Non-Monotonic Reasoning, Proceedings of the Second International Workshop, pages 23–42, Cambridge, Mass., July 1993. Lisbon, MIT Press.

    Google Scholar 

  18. Colin Bell, Anil Nerode, Raymond T. Ng, and V. S. Subrahmanian. Mixed Integer Programming Methods for Computing Non-Monotonic Deductive Databases. Journal of the ACM, 41(6):1178–1215, November 1994.

    Article  MATH  MathSciNet  Google Scholar 

  19. Nicole Bidoit and Christine Froidevaux. General logical Databases and Programs: Default Logic Semantics and Stratification. Information and Computation, 91:15–54, 1991.

    Article  MATH  MathSciNet  Google Scholar 

  20. Nicole Bidoit and Christine Froidevaux. Negation by Default and unstratifiable logic Programs. Theoretical Computer Science, 78:85–112, 1991.

    Article  MATH  MathSciNet  Google Scholar 

  21. Roland N. Bol and L. Degerstedt. Tabulated resolution for well-founded semantics. In Proc. Int. Logic Programming Symposium'93, Cambridge, Mass., 1993. MIT Press.

    Google Scholar 

  22. Stefan Brass and Jürgen Dix. A disjunctive semantics based on unfolding and bottom-up evaluation. In Bernd Wolfinger, editor, Innovationen bei Rechen-und Kommunikationssystemen, (IFIP '94-Congress, Workshop FG2: Disjunctive Logic Programming and Disjunctive Databases), pages 83–91, Berlin, 1994. Springer.

    Google Scholar 

  23. Stefan Brass and Jürgen Dix. A General Approach to Bottom-Up Computation of Disjunctive Semantics. In J. Dix, L. Pereira, and T. Przymusinski, editors, Non-monotonic Extensions of Logic Programming, LNAI 927, pages 127–155. Springer, Berlin, 1995.

    Google Scholar 

  24. Stefan Brass and Jürgen Dix. Characterizations of the Stable Semantics by Partial Evaluation. In A. Nerode, W. Marek, and M. Truszczyński, editors, Logic Programming and Non-Monotonic Reasoning, Proceedings of the Third International Conference, LNCS 928, pages 85–98, Berlin, June 1995. Springer.

    Google Scholar 

  25. Stefan Brass and Jürgen Dix. D-WFS: A Confluent calculus and an Equivalent Characterization. Technical Report TR 12/95, University of Koblenz, Department of Computer Science, Rheinau 1, September 1995.

    Google Scholar 

  26. 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, pages 199–213. MIT Press, June 1995.

    Google Scholar 

  27. Stefan Brass and Jürgen Dix. Characterizing D-WFS: Confluence and Iterated GCWA. In L.M. Pereira J.J. Alferes and E. Orlowska, editors, Logics in Artificial Intelligence (JELIA '96), LNCS 1126, pages 268–283. Springer, 1996. (Extended version will appear in the Journal of Automated Reasoning in 1998.).

    Google Scholar 

  28. Stefan Brass and Jürgen Dix. Characterizations of the Disjunctive Stable Semantics by Partial Evaluation. Journal of Logic Programming, 32(3):207–228, 1997. (Extended abstract appeared in: Characterizations of the Stable Semantics by Partial Evaluation LPNMR, Proceedings of the Third International Conference, Kentucky, pages 85–98, 1995. LNCS 928, Springer.).

    Article  MATH  MathSciNet  Google Scholar 

  29. Stefan Brass and Jürgen Dix. Characterizations of the Disjunctive Well-founded Semantics: Confluent Calculi and Iterated GCWA. Journal of Automated Reasoning, 20(1):143–165, 1998. (Extended abstract appeared in: Characterizing D-WFS: Confluence and Iterated GCWA. Logics in Artificial Intelligence, JELIA '96, pages 268–283, 1996. Springer, LNCS 1126.).

    Article  MATH  MathSciNet  Google Scholar 

  30. Stefan Brass and Jürgen Dix. Semantics of (Disjunctive) Logic Programs Based on Partial Evaluation. Journal of Logic Programming, accepted for publication, 1998. (Extended abstract appeared in: Disjunctive Semantics Based upon Partial and Bottom-Up Evaluation, Proceedings of the 12-th International Logic Programming Conference, Tokyo, pages 199–213, 1995. MIT Press.).

    Google Scholar 

  31. Stefan Brass, Jürgen Dix, Burkhard Freitag, and Zukowski. Transformation-based bottom-up computation of the well-founded model. Journal of Logic Programming, to appear, 1999.

    Google Scholar 

  32. Stefan Brass, Jürgen Dix, Ilkka NiemelÄ, and Teodor. C. Przymusinski. A Comparison of the Static and the Disjunctive Well-founded Semantics and its Implementation. In A. G. Cohn, L. K. Schubert, and S. C. Shapiro, editors, Principles of Knowledge Representation and Reasoning: Proceedings of the Sixth International Conference (KR '98), pages 74–85. San Francisco, CA, Morgan Kaufmann, May 1998. appeared also as TR 17/97, University of Koblenz.

    Google Scholar 

  33. Stefan Brass, Jürgen Dix, and Teodor. C. Przymusinski. Super Logic Programs. In L. C. Aiello, J. Doyle, and S. C. Shapiro, editors, Principles of Knowledge Representation and Reasoning: Proceedings of the Fifth International Conference (KR '96), pages 529–541. San Francisco, CA, Morgan Kaufmann, 1996.

    Google Scholar 

  34. Stefan Brass, Ulrich Zukowski, and Burkhardt Freitag. Transformation Based Bottom-Up Computation of the Well-Founded Model. In J. Dix, L. Pereira, and T. Przymusinski, editors, Nonmonotonic Extensions of Logic Programming, LNAI 1216, pages 171–201. Springer, Berlin, 1997.

    Google Scholar 

  35. G. Brewka. Adding priorities and specificity to default logic. In Logics in Artificial Intelligence, Proc. JELIA-94, York. Springer, 1994.

    Google Scholar 

  36. Gerd Brewka, Jürgen Dix, and Kurt Konolige. Nonmonotonic Reasoning: An Overview. CSLI Lecture Notes 73. CSLI Publications, Stanford, CA, 1997.

    Google Scholar 

  37. Gerhard Brewka. Well-founded semantics for extended logic programs with dynamic preferences. Journal of Artificial Intelligence Research, 4:19–36, 1996.

    MATH  MathSciNet  Google Scholar 

  38. Gerhard Brewka and Thomas Eiter. Preferred answer sets. In Anthony Cohn, Lenhart Schubert, and Stuart Shapiro, editors, Proceedings of the 6th Conference on Principles of Knowledge Representation and Reasoning, Trent, Italy, pages 86–97. Morgan Kaufmann, 1998.

    Google Scholar 

  39. FranÇois Bry. Query evaluation in recursive databases: bottom-up and top-down reconciled. Data & Knowledge Engineering, 5:289–312, 1990.

    Article  Google Scholar 

  40. M. Cadoli, F. M. Donini, P. Liberatore, and M. Schaerf. The size of a revised knowledge base. In PODS '95, pages 151–162, 1995.

    Google Scholar 

  41. Marco Cadoli, Francesco M. Donini, and Marco Schaerf. Is intractability of non-monotonic reasoning a real drawback? Artificial Intelligence Journal, 88:215–251, 1996.

    Article  MATH  MathSciNet  Google Scholar 

  42. Marco Cadoli, Francesco M. Donini, Marco Schaerf, and Riccardo Silvestri. On compact representations of prepositional circumscription. Theoretical Computer Science, 182:183–202, 1997. (Extended abstract appeared in: On Compact Representations of Propositional Circumscription. STACS '95, pages 205–216, 1995.).

    Article  MATH  MathSciNet  Google Scholar 

  43. L. Cavedon and J.W. Lloyd. A Completeness Theorem for SLDNF-Resolution. Journal of Logic Programming, 7:177–191, 1989.

    Article  MATH  MathSciNet  Google Scholar 

  44. David Chan. Constructive negation based on the completed database. In Proc. 1988 Conf. and Symp. on Logic Programming, pages 111–125, September 1988.

    Google Scholar 

  45. David Chan and Mark Wallace. An Experiment with programming using pure Negation. Technical Report TR, ECRC, July 1989.

    Google Scholar 

  46. Weidong Chen, Terrance Swift, and David S. Warren. Efficient Top-Down Computation of Queries under the Well-Founded Semantics. Journal of Logic Programming, 24(3):219–245, 1995.

    Article  MathSciNet  Google Scholar 

  47. Weidong Chen and David S. Warren. A Goal Oriented Approach to Computing The Well-founded Semantics. Journal of Logic Programming, 17:279–300, 1993.

    Article  MATH  MathSciNet  Google Scholar 

  48. Weidong Chen and David S. Warren. Computing of Stable Models and its Integration with Logical Query Processing. IEEE Transactions on Knowledge and Data Engineering, 17:279–300, 1995.

    MathSciNet  Google Scholar 

  49. Weidong Chen and David S. Warren. Tabled Evaluation with Delaying for General Logic Programs. Journal of the ACM, 43(1):20–74, January 1996.

    Article  MATH  MathSciNet  Google Scholar 

  50. Keith L. Clark. Negation as Failure. In H. Gallaire and J. Minker, editors, Logic and Data-Bases, pages 293–322. Plenum, New York, 1978.

    Google Scholar 

  51. A. Colmerauer, H. Kanoui, R. Pasero, and P. Roussel. Un système de communication homme-machine en franÇais. Technical report, Groupe de Intelligence Artificielle Universite de Aix-Marseille II, 1973.

    Google Scholar 

  52. Stefania Costantini and Gaetano A. Lanzarone. Static Semantics as Program Transformation and Well-founded Computation. In J. Dix, L. Pereira, and T. Przymusinski, editors, Nonmonotonic Extensions of Logic Programming, LNAI 927, pages 156–180. Springer, Berlin, 1995.

    Google Scholar 

  53. Lars Degerstedt and Ulf Nilsson. Magic Computation of Well-founded Semantics. In J. Dix, L. Pereira, and T. Przymusinski, editors, Nonmonotonic Extensions of Logic Programming, LNAI 927, pages 181–204. Springer, Berlin, 1995.

    Google Scholar 

  54. J. Dix and U. Furbach. The DFG-Project DisLoP on Disjunctive Logic Programming. Computational Logic, 2(2):89–90, 1996.

    Google Scholar 

  55. J. Dix, U. Furbach, and A. Nerode, editors. Logic Programming and Nonmonotonic Reasoning, LNAI 1265, Berlin, 1997. Springer.

    Google Scholar 

  56. Jürgen Dix. Classifying Semantics of Logic Programs. In Anil Nerode, Wiktor Marek, and V. S. Subrahmanian, editors, Logic Programming and Non-Monotonic Reasoning, Proceedings of the first International Workshop, pages 166–180, Cambridge, Mass., July 1991. Washington D.C, MIT Press.

    Google Scholar 

  57. 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.

    Google Scholar 

  58. Jürgen Dix. Classifying Semantics of Disjunctive Logic Programs. In K. R. Apt, editor, LOGIC PROGRAMMING: Proceedings of the 1992 Joint International Conference and Symposium, pages 798–812, Cambridge, Mass., November 1992. MIT Press.

    Google Scholar 

  59. Jürgen Dix. A Classification-Theory of Semantics of Normal Logic Programs: I. Strong Properties. Fundamenta Informaticae, XXII(3):227–255, 1995.

    MathSciNet  Google Scholar 

  60. Jürgen Dix. A Classification-Theory of Semantics of Normal Logic Programs: II. Weak Properties. Fundamenta Informaticae, XXII(3):257–288, 1995.

    MathSciNet  Google Scholar 

  61. Jürgen Dix. Semantics of Logic Programs: Their Intuitions and Formal Properties. An Overview. In Andre Fuhrmann and Hans Rott, editors, Logic, Action and Information — Essays on Logic in Philosophy and Artificial Intelligence, pages 241–327. DeGruyter, 1995.

    Google Scholar 

  62. Jürgen Dix, Donald Loveland, Jack Minker, and David. S. Warren. Disjunctive Logic Programming and databases: Nonmonotonic Aspects. Technical Report Dagstuhl Seminar Report 150, IBFI GmbH, Schlo\ Dagstuhl, 1996.

    Google Scholar 

  63. Jürgen Dix and Martin Müller. Abstract Properties and Computational Complexity of Semantics for Disjunctive Logic Programs. In Proc. of the Workshop W1, Structural Complexity and Recursion-theoretic Methods in Logic Programming, following the JICSLP '92, pages 15–28. H. Blair and W. Marek and A. Nerode and J. Remmel, November 1992. also available as Technical Report 13/93, University of Koblenz, Department of Computer Science.

    Google Scholar 

  64. Jürgen Dix and Martin Müller. Implementing Semantics for Disjunctive Logic Programs Using Fringes and Abstract Properties. In Luis Moniz Pereira and Anil Nerode, editors, Logic Programming and Non-Monotonic Reasoning, Proceedings of the Second International Workshop, pages 43–59, Cambridge, Mass., July 1993. Lisbon, MIT Press.

    Google Scholar 

  65. Jürgen Dix and Frieder Stolzenburg. Computation of Non-Ground Disjunctive Well-Founded Semantics with Constraint Logic Programming (preliminary report). In J. Dix, L. Pereira, and T. Przymusinski, editors, Nonmonotonic Extensions of Logic Programming, LNAI 1216, pages 202–226. Springer, Berlin, 1997.

    Google Scholar 

  66. Jürgen Dix and Frieder Stolzenburg. A Framework to incorporate Nonmonotonic Reasoning into Constraint Logic Programming. Journal of Logic Programming, 35(1,2,3):5–37, 1998. Special Issue on Constraint Logic Programming, Guest Editors: Kim Marriott and Peter Stuckey.

    MathSciNet  Google Scholar 

  67. Wlodzimierz Drabent. What is failure? A constructive approach to negation. Acta Informatica, 32(1):27–29, 1994.

    Article  MathSciNet  Google Scholar 

  68. P. M. Dung. On the relations between stable and wellfounded semantics of logic programs. Theoretical Computer Science, 105:7–25, 1992.

    Article  MATH  MathSciNet  Google Scholar 

  69. T. Eiter, J. Lu, and V. S. Subrahmanian. Computing Non-Ground Representations of Stable Models. In J. Dix, U. Furbach, and A. Nerode, editors, Logic Programming and Non-Monotonic Reasoning, Proceedings of the Fourth International Conference, LNAI 1265, pages 198–217, Berlin, July 1997. Springer.

    Google Scholar 

  70. F. Fages. Consistency of Clark's completion and existence of stable models. Methods of Logic in Computer Science, 2, 1993.

    Google Scholar 

  71. J. A. Fernández, J. Lobo, J. Minker, and V.S. Subrahmanian. Disjunctive LP + Integrity Constraints = Stable Model Semantics. Annals of Mathematics and Artificial Intelligence, 8(3–4), 1993.

    Google Scholar 

  72. J. A. Fernández and J. Minker. Bottom-Up Computation of Perfect Models for Disjunctive Theories. Journal of Logic Programming, 25(1):33–51, 1995.

    Article  MATH  MathSciNet  Google Scholar 

  73. Michael Gelfond and Vladimir Lifschitz. The Stable Model Semantics for Logic Programming. In R. Kowalski and K. Bowen, editors, 5th Conference on Logic Programming, pages 1070–1080. MIT Press, 1988.

    Google Scholar 

  74. Goran Gogic, Christos Papadimitriou, Bart Selman, and Henry Kautz. The Comparative Linguistics of Knowledge Representation. In Proceedings of the 14th International Joint Conference on Artificial Intelligence, pages 862–869, Montreal, Canada, August 1995. Morgan Kaufmann Publishers.

    Google Scholar 

  75. T. F. Gordon. The Pleadings Game: An Artificial Intelligence Model of Procedural Justice. PhD thesis, TU Darmstadt, 1993.

    Google Scholar 

  76. Jeff Horty, Richmond Thomason, and D. S. Touretzky. A skeptical Theory of Inheritance in Nonmonotonic Semantic Networks. Artificial Intelligence, 42:311–348, 1990.

    Article  MATH  MathSciNet  Google Scholar 

  77. Katsumi Inoue, M. Koshimura, and R. Hasegawa. Embedding negation-as-failure into a model generation theorem prover. In Deepak Kapur, editor, Automated Deduction — CADE-11, number 607 in LNAI, Berlin, 1992. Springer.

    Google Scholar 

  78. Vadim Kagan, Anil Nerode, and V. S. Subrahmanian. Computing Definite Logic Programs by Partial Instantiation. Annals of Pure and Applied Logic, 67:161–182, 1994.

    Article  MATH  MathSciNet  Google Scholar 

  79. Vadim Kagan, Anil Nerode, and V. S. Subrahmanian. Computing Minimal Models by Partial Instantiation. Theoretical Computer Science, 155:157–177, 1995.

    Article  MathSciNet  Google Scholar 

  80. David B. Kemp, Peter J. Stuckey, and Divesh Srivastava. Magic Sets and Bottom-Up Evaluation of Well-Founded Models. In Vijay Saraswat and Kazunori Ueda, editors, Proceedings of the 1991 Int. Symposium on Logic Programming, pages 337–351. MIT, June 1991.

    Google Scholar 

  81. Kurt Konolige. Partial Models and Non-Monotonic Reasoning. In J. Richards, editor, The Logic and Aquisition of Knowledge. Oxford Press, 1988.

    Google Scholar 

  82. R.A. Kowalski. Predicate logic as a programming language. In Proceeedings IFIP' 74, pages 569–574. North Holland Publishing Company, 1974.

    Google Scholar 

  83. V. Lifschitz. Foundations of declarative logic programming. In G. Brewka, editor, Principles of Knowledge Representation, chapter 3, pages 69–128. CSLI, 1996.

    Google Scholar 

  84. Vladimir Lifschitz. Computing Circumscription. In Proceedings of the International Joint Conference on Artificial Intelligence, Los Angeles, California, pages 121–127, 1985.

    Google Scholar 

  85. John W. Lloyd. Foundations of Logic Programming. Springer, Berlin, 1987. 2nd edition.

    Google Scholar 

  86. Bertram LudÄscher. CNF-Prolog: A Meta-Interpreter for Chan's Constructive Negation, Implementation. Technical report, Master Thesis, Karlsruhe University (in german), 1991.

    Google Scholar 

  87. Jack Minker. On indefinite databases and the closed world assumption. In Proceedings of the 6th Conference on Automated Deduction, New York, pages 292–308, Berlin, 1982. Springer.

    Google Scholar 

  88. Jack Minker. Foundations of Deductive Databases. Morgan Kaufmann, 95 First Street, Los Altos, CA 94022, 1st edition, 1988.

    Google Scholar 

  89. Jack Minker. An Overview of Nonmonotonic Reasoning and Logic Programming. Journal of Logic Programming, Special Issue, 17(2/3/4):95–126, 1993.

    Article  MATH  MathSciNet  Google Scholar 

  90. Jack Minker and Carolina Ruiz. Computing stable and partial stable models of extended disjunctive logic programs. In J. Dix, L. Pereira, and T. Przymusinski, editors, Nonmonotonic Extensions of Logic Programming, LNAI 927, pages 205–229. Springer, Berlin, 1995.

    Google Scholar 

  91. Martin Müller. Examples and Run-Time Data from KORF, 1992.

    Google Scholar 

  92. Martin Müller and Jürgen Dix. Implementing Semantics for Disjunctive Logic Programs Using Fringes and Abstract Properties. In Luis Moniz Pereira and Anil Nerode, editors, Logic Programming and Non-Monotonic Reasoning, Proceedings of the Second International Workshop, pages 43–59, Cambridge, Mass., July 1993. Lisbon, MIT Press.

    Google Scholar 

  93. Anil Nerode, Raymond T. Ng, and V.S. Subrahmanian. Computing Circumscriptive Deductive Databases. CS-TR 91-66, Computer Science Dept., Univ. Maryland, University of Maryland, College Park, Maryland, 20742, USA, December 1991.

    Google Scholar 

  94. Ilkka NiemelÄ. Implementing circumscription using a tableau method. In W. Wahlster, editor, Proceedings of the European Conference on Artificial Intelligence, pages 80–84, Budapest, Hungary, August 1996. John Wiley.

    Google Scholar 

  95. Ilkka NiemelÄ. A tableau calculus for minimal model reasoning. In P. Miglioli, U. Moscato, D. Mundici, and M. Ornaghi, editors, Proceedings of the Fifth Workshop on Theorem Proving with Analytic Tableaux and Related Methods, pages 278–294, Terrasini, Italy, May 1996. LNAI 1071, Springer-Verlag.

    Google Scholar 

  96. Ilkka NiemelÄ and Patrik Simons. Efficient Implementation of the Well-founded and Stable Model Semantics. In M. Maher, editor, Proceedings of the Joint International Conference and Symposium on Logic Programming, pages 289–303, Bonn, Germany, September 1996. The MIT Press.

    Google Scholar 

  97. L. M. Pereira, J. N. Aparício, and J. J. Alferes. Non-Monotonic Reasoning with Logic Programming. Journal of Logic Programming, 17:227–264, 1993.

    Article  MATH  MathSciNet  Google Scholar 

  98. L.M. Pereira and J.J. Alferes. Well founded semantics for logic programs with explicit negation. In Bernd Neumann, editor, Proc. of 10th European Conf. on Artificial Intelligence ECAI 92, pages 102–106. John Wiley & Sons, 1992.

    Google Scholar 

  99. D. Poole. On the comparison of theories: Preferring the most specific explanation. In Proc. IJCAI-85, Los Angeles, 1985.

    Google Scholar 

  100. H. Prakken. Logical Tools for Modelling Legal Argument. PhD thesis, VU Amsterdam, 1993.

    Google Scholar 

  101. Teodor Przymusinski. Stationary Semantics for Normal and Disjunctive Logic Programs. In C. Delobel, M. Kifer, and Y. Masunaga, editors, DOOD '91, Proceedings of the 2nd International Conference, Berlin, December 1991. Muenchen, Springer. LNCS 566.

    Google Scholar 

  102. Raymond Reiter. On closed world data bases. In Hervé Gallaire and Jack Minker, editors, Logic and Data Bases, pages 55–76, New York, 1978. Plenum.

    Google Scholar 

  103. Raymond Reiter. A Logic for Default-Reasoning. Artificial Intelligence, 13:81–132, 1980.

    Article  MATH  MathSciNet  Google Scholar 

  104. Stuart Russel and Peter Norvig. Artificial Intelligence — A Modern Approach. Prentice Hall, New Jersey 07458, 1995.

    Google Scholar 

  105. Ch. Sakama and K. Inoue. An Alternative Approach to the Semantics of Disjunctive Logic Programs and Deductive Databases. Journal of Automated Reasoning, 13:145–172, 1994.

    Article  MATH  MathSciNet  Google Scholar 

  106. Chiaki Sakama and Hirohisa Seki. Partial Deduction of Disjunctive Logic Programs: A Declarative Approach. In Logic Program Synthesis and Transformation — Meta Programming in Logic, LNCS 883, pages 170–182, Berlin, 1994. Springer.

    Google Scholar 

  107. Chiaki Sakama and Hirohisa Seki. Partial Deduction in Disjunctive Logic Programming. Journal of Logic Programming, 32(3):229–245, 1997.

    Article  MATH  MathSciNet  Google Scholar 

  108. H. Tamaki and T. Sato. OLD Resolution with Tabulation. In Proceedings of the Third International Conference on Logic Programming, London, LNAI, pages 84–98, Berlin, June 1986. Springer.

    Google Scholar 

  109. A. Tarski. A lattice-theoretical fixpoint theorem and its applications. Pacific Journal of Mathematics, 5:285–309, 1955.

    MATH  MathSciNet  Google Scholar 

  110. D. S. Touretzky. The Mathematics of Inheritance. Research Notes in Artificial Intelligence. Pitman, London, 1986.

    Google Scholar 

  111. D. S. Touretzky, R. H. Thomason, and J. P. Horty. A skeptic's menagerie: Conflictors, preemptors, reinstaters, and zombies in nonmonotonic inheritance. In Proc. 12th IJCAI, Sydney, 1991.

    Google Scholar 

  112. David S. Touretzky, Jeff Horty, and Richmond Thomason. A Clash of Intuitions: The current State of Nonmonotonic Multiple IHS. In Proceedings IJCAJ, 1988.

    Google Scholar 

  113. Jeffrey D. Ullman. Bottom-up Beats Top-down for Datalog. In Proc. of the Eight ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Database Systems, Philadelphia, Pennsylvania, pages 140–149. ACM Press, March 1989.

    Google Scholar 

  114. Jeffrey D. Ullman. Principles of Database and Knowledge-Base Systems, Vol. 2. Computer Science Press, Rockville, 1989.

    Google Scholar 

  115. M.H. van Emden and R.A. Kowalski. The semantics of predicate logic as a programming language. JACM, 23:733–742, 1976.

    Article  MATH  Google Scholar 

  116. Allen Van Gelder, Kenneth A. Ross, and J. S. Schlipf. Unfounded Sets and well-founded Semantics for general logic Programs. In Proceedings 7th Symposion on Principles of Database Systems, pages 221–230, 1988.

    Google Scholar 

  117. Martin Vorbeck. CNF-Prolog: A Meta-Interpreter for Chan's Constructive Negation, Theory. Technical report, Master Thesis, Karlsruhe University (in german), 1991.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Jürgen Dix Luís Moniz Pereira Teodor C. Przymusinski

Rights and permissions

Reprints and permissions

Copyright information

© 1998 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Brewka, G., Dix, J. (1998). Knowledge representation with logic programs. In: Dix, J., Pereira, L.M., Przymusinski, T.C. (eds) Logic Programming and Knowledge Representation. LPKR 1997. Lecture Notes in Computer Science, vol 1471. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0054788

Download citation

  • DOI: https://doi.org/10.1007/BFb0054788

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-64958-8

  • Online ISBN: 978-3-540-49872-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics