Higher-order Concepts in a Tractable Knowledge Representation
Due to the intractability of providing the full set of higher-order logical inferences, the introduction of higher-order concepts Into knowledge representation formalisms is usually avoided. In fact, this needn’t be so. We present the knowledge representation of the knowledge acquisition system BLIP, and describe how higher-order concepts are represented by using metapredlcates We then show that metapredicates have the necessary properties to qualify for inclusion in a knowledge representation: they can be given a precise semantics, and allow a natural set of Inferences to be provided effectively. We specify the inference rules for the representation, and prove they are fact-complete and tractable.
KeywordsKnowledge Representation Inference Rule Atomic Formula Predicate Symbol Predicate Variable
Unable to display preview. Download preview PDF.
- Brachman, Ronald J., and Schmolze, J. G., An Overview of the KL-ONE Knowledge Representation System,“ in Cognitive Science. Vol., 9, 1985.Google Scholar
- Emde, Werner, “IM 2.0 - Eine Inferenzmaschine fur ein lernendes System,” forthcoming.Google Scholar
- Emde, Werner, and Mork. Katharina, “The BLIP system,” KIT-REPORT 32, Techn. Univ. Berlin, February 1986.Google Scholar
- Hebei, Christopher, and Rollinger, Claus-Rainer, “Aspekte der rechnergestutzten Generierung von lnferenzregeln durch Regelschemata,” in Proc. GWAI-81, ed. J. Siekmann, Springer-Verlag, Berlin, 1981.Google Scholar
- Hobbs, Jerry R., Discourse and inference, chapter 2, Draft, Stanford University, June, 1986.Google Scholar
- McCarthy, John, “First-order Theories of Individual Concepts and Propositions,” in Machine intelligence 9, ed. J. Hayes, D. Mlchie, and L. Mikulich, pp. 129–147, reprinted in Readings in Knowledge Representation, ed. R. Brachman and H. Levesque, pp. 523–533, Morgan Kaufman, Los Altos, CA, 1985.Google Scholar
- Mendelson, Elliot, introduction to MATHEMATICAL LOGIC, pp. 49ff, Van Nostrand, New York, 1964.Google Scholar
- Mork, Katharina, “Acquiring Domain Models,” in Proc. of the Knowledge Acquisition for Knowledge–Based Systems Workshop,pp. 32–0–32–15, Banff, Canada, Nov. 1986. (Also to appear in Int. Journal of Man–Machine Studies) Google Scholar
- Levesque, Hector J., and Brachman, Ronald. J., “A Fundamental Tradeoff in Knowledge Representation and Reasoning (Revised Version),” in Readings In Knowledge Representation, ed. R. Brachman and H. Levesque, pp. 41–70, Morgan Kaufman, Los Altos. CA, 1985.Google Scholar
- Nebel, Bernhard, “Computational Complexity of Terminological Reasoning in BACK,” forthcoming.Google Scholar
- Patel-Schneider, Peter F., “A Four-Valued Semantics for Frame-Based Description Languages,” In Proc. AAAI-86, pp. 344–348, Morgan Kaufman, Los Altos, CA, 1986.Google Scholar