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The Complexity of Concept Languages

Francesco M. Donini; Maurizio Lenzerini; Daniele Nardi; Werner Nutt
DFKI, DFKI Research Reports (RR), Vol. 95-07, 1995.


The basic feature of Terminological Knowledge Representation Systems is to represent knowledge by means of taxonomies, here called terminologies , and to provide a specialized reasoning engine to do inferences on these structures. The taxonomy is built through a representation language called concept language (or description logic), which is given well-defined set-theoretic semantics. The efficiency of reasoning has often been advocated as a primary motivation for the use of such systems. Deduction methods and computational properties of reasoning problems in concept languages are the subject of this paper. The main contributions of the paper are: (1) a complexity analysis of concept satisfiability and subsumption for a wide class of concept languages; (2) the algorithms for these inferences that comply with the worst-case complexity of the reasoning task they perform.