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Concept Logics

  • Franz Baader
  • Hans-Jürgen Bürckert
  • Bernhard Hollunder
  • Werner Nutt
  • Jörg H. Siekmann
Part of the ESPRIT Basic Research Series book series (ESPRIT BASIC)

Abstract

Concept languages (as used in BACK, KL-ONE, KRYPTON, LOOM) are employed as knowledge representation formalisms in Artificial Intelligence. Their main purpose is to represent the generic concepts and the taxonomical hierarchies of the domain to be modeled. This paper addresses the combination of the fast taxonomical reasoning algorithms (e.g. subsumption, the classifier etc.) that come with these languages and reasoning in first order predicate logic. The interface between these two different modes of reasoning is accomplished by a new rule of inference, called constrained resolution. Correctness, completeness as well as the decidability of the constraints (in a restricted constraint language) are shown.

Keywords

concept description languages KL-ONE constrained resolution taxonomical reasoning knowledge representation languages 

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References

  1. Baader, F.: “Regular Extensions of KL-ONE”, DFKI Research Report, forthcoming.Google Scholar
  2. Beierle, C., Hedtstück, U.,Pletat, U., Schmitt, P. H., Siekmann, J.: “An Order-Sorted Logic for Knowledge Representation Systems”, IWBS Report 113, IBM Deutschland, 1990.Google Scholar
  3. Brachman, R. J., Schmolze, J. G.: “An Overview of the KL-ONE Knowledge Representation System”, Cognitive Science, 9(2), pp. 171–216, 1985.CrossRefGoogle Scholar
  4. Brachman, R.J., Levesque, H.J.: Readings in Knowledge Representation. Morgan Kaufmann Publishers, 1985.zbMATHGoogle Scholar
  5. z, R.J., Pigman Gilbert, V., Levesque, H.J.: “An Essential Hybrid Reasoning System: Knowledge and Symbol Level Account in KRYPTON”, in Proceedings of the 9th IJCAI, pp. 532–539, Los Angeles, Cal., 1985.Google Scholar
  6. Bürckert, H.-J.: “A Resolution Principle for a Logic with Restricted Quantifiers”, Dissertation, Universität Kaiserslautern, Postfach 3049, D-6750 Kaiserslautern, West-Germany, 1990.Google Scholar
  7. Bürckert, H.-J.: “A Resolution Principle for Clauses with Constraints”, in Proceedings of 10th International Conference on Automated Deduction, Springer LNAI 449, pp. 178–192, 1990.Google Scholar
  8. Cohn, A. G.: “A More Expressive Formulation of Many-Sorted Logic”, JAR 3,2, pp. 113–200, 1987.zbMATHCrossRefGoogle Scholar
  9. Frisch, A.: “A General Framework for Sorted Deduction: Fundamental Results on Hybrid Reasoning”, in Proceedings of International Conference on Principles of Knowledge Representation and Reasoning, pp. 126–136, 1989.Google Scholar
  10. Frisch, A.: “An Investigation into Inference with Restricted Quantification and Taxonomic Representation”, Logic Programming Newsletters, 6, pp. 5–8, 1986.Google Scholar
  11. Höhfeld, M., Smolka, G.: “Definite Relations over Constraint Languages”, LILOG-Report 53, IBM Deutschland, 1988.Google Scholar
  12. Hollunder, B.: “Hybrid Inferences in KL-ONE-based Knowledge Representation Systems”, DFKI Research Report RR-90–06, DFKI, Postfach 2080, D-6750 Kaiserslautern, West-Germany, 1990.Google Scholar
  13. Hollunder, B.: “Hybrid Inferences in KL-ONE-based Knowledge Representation Systems”, in the Proceedings of the 14th German Workshop on Artificial Intelligence, Springer-Verlag, 1990.Google Scholar
  14. Hollunder, B., Nutt, W.: “Subsumption Algorithms for Concept Languages”, DFKI Research Report RR-90–04, DFKI, Postfach 2080, D-6750 Kaiserslautern, West-Germany, 1990.Google Scholar
  15. Hollunder, B., Nutt, W.: “Subsumption Algorithms for Concept Languages” in the Proceedings of the 9th European Conference on Artificial Intelligence, Pitman Publishing, 1990.Google Scholar
  16. Huet, G.: “Constrained Resolution — A Complete Method for Higher Order Logic”, Ph.D. Thesis, Case Western University, 1972.Google Scholar
  17. Jaffar, J., Lassez, J.-L.: “Constrained Logic Programming”, Proceedings of ACM Symp. on Principles of Programming Languages, 111–119, 1987.Google Scholar
  18. Levesque, H. J., Brachman, R. J.: “Expressiveness and Tractability in Knowledge Representation and Reasoning”, Computational Intelligence, 3, pp. 78–93, 1987.CrossRefGoogle Scholar
  19. MacGregor, R., Bates, R.: “The Loom Knowledge Representation Language”, Technical Report ISI/RS-87–188, University of Southern California, Information Science Institute, Marina del Rey, Cal., 1987.Google Scholar
  20. Nebel, B.: “Reasoning and Revision in Hybrid Representation Systems”, Lecture Notes in Artificial Intelligence, LNAI 422, Springer-Verlag, 1990.zbMATHGoogle Scholar
  21. Oberschelp, A.: “Untersuchungen zur mehrsortigen Quantorenlogik”, Mathematische Annalen, 145:297–333, 1962.MathSciNetzbMATHCrossRefGoogle Scholar
  22. Quillian, R. M.: “Semantic Memory”, in Semantic Information Processing (ed. M. Minsky), pp. 216–270, MIT-Press, 1968.Google Scholar
  23. Robinson, J.A.: “A Machine Oriented Logic Based on the Resolution Principle”, J. ACM, 12(1), pp. 23–41, 1965.zbMATHCrossRefGoogle Scholar
  24. Schmidt, A.: “Ueber deduktive Theorien mit mehreren Sorten von Grunddingen”, Mathematische Annalen, 115:485–506, 1938.MathSciNetCrossRefGoogle Scholar
  25. Schmidt, A.: “Die Zulässigkeit der Behandlung mehrsortiger Theorien mittels der üblichen einsortigen Prädikatenlogik”, Mathematische Annalen, 123:187–200, 1951.MathSciNetzbMATHCrossRefGoogle Scholar
  26. Schmidt-Schauß, M., Smolka, G.: “Attributive Concept Descriptions with Unions and Complements”, SEKI Report SR-88–21, FB Informatik, University of Kaiserslautern, West Germany, 1988. To appear in Artificial Intelligence.Google Scholar
  27. Schmidt-Schauß, M.: “Computational Aspects of an Order-sorted Logic with Term Declarations”, Lecture Notes on Artificial Intelligence, LNAI 395, Springer, 1989zbMATHCrossRefGoogle Scholar
  28. Smolka, G.: “Logic Programming over Polymorphically Order-sorted Types”, Dissertation, Universität Kaiserslautern, 1989.Google Scholar
  29. Stickel, M. E.: “Automated Deduction by Theory Resolution”, Journal of Automated Reasoning, 1:333–355, 1985.MathSciNetzbMATHCrossRefGoogle Scholar
  30. Vilain., M. B.: “The Restricted Language Architecture of a Hybrid Representation System”, in Proceeding of the 9th IJCAI, pp. 547–551, Los Angeles, Cal., 1985.Google Scholar
  31. Walther, C.: “A Many-sorted Calculus Based on Resolution and Paramodulation”, Research Notes in Artificial Intelligence, Pitman, Morgan Kaufman Publishers, 1987.zbMATHGoogle Scholar
  32. Walther, C.: “Many-Sorted Unification”, J. ACM, 35(1), pp. 1–17, 1988.MathSciNetCrossRefGoogle Scholar
  33. Weidenbach, C., Ohlbach H.-J.: “A Resolution Calculus with Dynamic Sort Structures and Partial Functions”, Proceedings of the 9th European Conference on Artificial Intelligence, Pitman Publishing, 1990.Google Scholar

Copyright information

© ECSC — EEC — EAEC, Brussels — Luxembourg 1990

Authors and Affiliations

  • Franz Baader
    • 1
  • Hans-Jürgen Bürckert
    • 1
  • Bernhard Hollunder
    • 1
  • Werner Nutt
    • 1
  • Jörg H. Siekmann
    • 2
  1. 1.Projektgruppe WINODFKI KaiserslauternKaiserslauternFR Germany
  2. 2.FB InformatikUniversität KaiserslauternKaiserslauternFR Germany

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