Defeasible Description Logics

Abstract

Abstract. We propose to extend description logic with defeasible rules, and to use the inferential mechanism of defeasible logic to reason with description logic constructors.

Practical Reasoning for Defeasible Description Logics

“…The approach by Governatori [81] appears a more natural combination of defeasible logic with DLs. The set of ABox statements in the DL KB constitutes the facts in a defeasible logic theory, the subsumptions are translated into strict rules and defeasibility is introduced by adding standard defeasible rules to the theory.…”

$\mathcal{ALE}$ Defeasible Description Logic

“…In this section, we introduce an ALC − defeasible description logic [3], i.e., an extension of ALC − description logic with defeasible logic. Also, we introduce several adjustments for the logic.…”

“…In fact, the Tbox T corresponds to the set of strict rules in defeasible logic. Governatori [3] shows how can we transform ALC − Tbox to a set of strict rules, using a set of axiom pairs and a procedure ExtractRules. Basically, an inclusion axiom:…”

“…Defeasible logic is proved to have well behavior: 1) coherence and 2) consistence [3,2]. Furthermore, the consequences of a propositional defeasible theory D can be derived in O(N) time, where N is the number of propositional literals in D [4].…”

“…The procedure then returns a transformed defeasible theory D b . Given a basic defeasible theory D b , defeasible proof conditions in [3] are simplified as follows:…”