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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Baader, F.: “Regular Extensions of KL-ONE”, DFKI Research Report, forthcoming.
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.
Brachman, R. J., Schmolze, J. G.: “An Overview of the KL-ONE Knowledge Representation System”, Cognitive Science, 9(2), pp. 171–216, 1985.
Brachman, R.J., Levesque, H.J.: Readings in Knowledge Representation. Morgan Kaufmann Publishers, 1985.
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.
Bürckert, H.-J.: “A Resolution Principle for a Logic with Restricted Quantifiers”, Dissertation, Universität Kaiserslautern, Postfach 3049, D-6750 Kaiserslautern, West-Germany, 1990.
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.
Cohn, A. G.: “A More Expressive Formulation of Many-Sorted Logic”, JAR 3,2, pp. 113–200, 1987.
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.
Frisch, A.: “An Investigation into Inference with Restricted Quantification and Taxonomic Representation”, Logic Programming Newsletters, 6, pp. 5–8, 1986.
Höhfeld, M., Smolka, G.: “Definite Relations over Constraint Languages”, LILOG-Report 53, IBM Deutschland, 1988.
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.
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.
Hollunder, B., Nutt, W.: “Subsumption Algorithms for Concept Languages”, DFKI Research Report RR-90–04, DFKI, Postfach 2080, D-6750 Kaiserslautern, West-Germany, 1990.
Hollunder, B., Nutt, W.: “Subsumption Algorithms for Concept Languages” in the Proceedings of the 9th European Conference on Artificial Intelligence, Pitman Publishing, 1990.
Huet, G.: “Constrained Resolution — A Complete Method for Higher Order Logic”, Ph.D. Thesis, Case Western University, 1972.
Jaffar, J., Lassez, J.-L.: “Constrained Logic Programming”, Proceedings of ACM Symp. on Principles of Programming Languages, 111–119, 1987.
Levesque, H. J., Brachman, R. J.: “Expressiveness and Tractability in Knowledge Representation and Reasoning”, Computational Intelligence, 3, pp. 78–93, 1987.
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.
Nebel, B.: “Reasoning and Revision in Hybrid Representation Systems”, Lecture Notes in Artificial Intelligence, LNAI 422, Springer-Verlag, 1990.
Oberschelp, A.: “Untersuchungen zur mehrsortigen Quantorenlogik”, Mathematische Annalen, 145:297–333, 1962.
Quillian, R. M.: “Semantic Memory”, in Semantic Information Processing (ed. M. Minsky), pp. 216–270, MIT-Press, 1968.
Robinson, J.A.: “A Machine Oriented Logic Based on the Resolution Principle”, J. ACM, 12(1), pp. 23–41, 1965.
Schmidt, A.: “Ueber deduktive Theorien mit mehreren Sorten von Grunddingen”, Mathematische Annalen, 115:485–506, 1938.
Schmidt, A.: “Die Zulässigkeit der Behandlung mehrsortiger Theorien mittels der üblichen einsortigen Prädikatenlogik”, Mathematische Annalen, 123:187–200, 1951.
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.
Schmidt-Schauß, M.: “Computational Aspects of an Order-sorted Logic with Term Declarations”, Lecture Notes on Artificial Intelligence, LNAI 395, Springer, 1989
Smolka, G.: “Logic Programming over Polymorphically Order-sorted Types”, Dissertation, Universität Kaiserslautern, 1989.
Stickel, M. E.: “Automated Deduction by Theory Resolution”, Journal of Automated Reasoning, 1:333–355, 1985.
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.
Walther, C.: “A Many-sorted Calculus Based on Resolution and Paramodulation”, Research Notes in Artificial Intelligence, Pitman, Morgan Kaufman Publishers, 1987.
Walther, C.: “Many-Sorted Unification”, J. ACM, 35(1), pp. 1–17, 1988.
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.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1990 ECSC — EEC — EAEC, Brussels — Luxembourg
About this paper
Cite this paper
Baader, F., Bürckert, HJ., Hollunder, B., Nutt, W., Siekmann, J.H. (1990). Concept Logics. In: Lloyd, J.W. (eds) Computational Logic. ESPRIT Basic Research Series. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-76274-1_10
Download citation
DOI: https://doi.org/10.1007/978-3-642-76274-1_10
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-76276-5
Online ISBN: 978-3-642-76274-1
eBook Packages: Springer Book Archive