Subsumption in knowledge graphs
An important notion for representation formalisms of natural language semantics, is a subsumption hierarchy. Therefore a precise definition of subsumption is necessary. We shall argue that the usual solution of providing an extensional semantics and mapping subsumption onto set-inclusion, is not satisfactory. The problem is that extensions lose track of the structure. A better solution is used for conceptual graphs , where derivation rules define generalization.
In this paper we shall introduce knowledge graphs, and give a definition of subsumption, that does keep track of the structure. Moreover, because structural subsumption can be tested with a tractable algorithm, the fundamental tradeoff between expressiveness and complexity of inferences  does not occur.
Unable to display preview. Download preview PDF.
- A.R. Anderson and N.D. Belnap. Entailment: The Logic of Relevance and Necessity. Princeton University Press, Princeton, 1975.Google Scholar
- R. R. Bakker. Knowledge Graphs: representation and structuring of scientific knowledge. PhD thesis, University of Twente, Enschede, 1987.Google Scholar
- J. Barwise and J. Perry. Situations and Attitudes. MIT Press, 1983.Google Scholar
- R. J. Brachman. On the epistemological status of semantic networks. In N. V. Findler, editor, Associative Networks Representation and Use of Knowledge by Computers, pages 3–50. Academic Press, Inc., 1979.Google Scholar
- R. J. Brachman and H. J. Levesque. The tractability of subsumption in frame-based description languages. In Proceedings of AAAI-84, pages 34–37. Austin, 1984.Google Scholar
- B. Hollunder, W. Nutt, and M. Schmidt-Schauß. Subsumption algorithms for conception description languages. In Proceedings of 9th European Conference on Artificial Intelligence, London, 1990, Pitman Publishing.Google Scholar
- M.K. Jackman. Inference and the conceptual graph knowledge representation language. In S. Moralee, editor, Research and development in Expert Systems IV, Proceedings of Expert Systems '87. Cambridge University Press, 1988.Google Scholar
- M. Kay. Parsing in functional unification grammar. In D. Dowty, L. Kartunnen, and A. Zwicky, editors, Natural Language Parsing. Cambridge University Press, 1985.Google Scholar
- H. J. Levesque and R. J. Brachman. A fundamental tradeoff in knowledge representation and reasoning. In R. J. Brachman and H. J. Levesque, editors, Readings in Knowledge Representation, pages 41–70. Morgan Kaufmann Publishers, Inc., 1985.Google Scholar
- M. Schmidt-Schauß. Subsumption in KL-ONE is undecidable. In R. Brachman, H. Levesque, and R. Reiter, editors, Proceedings of First International Conference on Knowledge Representation and Reasoning. Morgan Kaufmann Publishers, Inc., 1989.Google Scholar
- J.G. Schmolze. Terminological knowledge representation systems. In R. Brachman, H. Levesque, and R. Reiter, editors, Proceedings of First International Conference on Knowledge Representation and Reasoning. Morgan Kaufmann Publishers, Inc., 1989.Google Scholar
- J. F. Sowa. Conceptual Structures: Information Processing in Mind and Machine. Addison-Wesley, Reading, 1984.Google Scholar