A Strong Correspondence between Description Logics and Open Logic Programming

This paper formally investigates the relationship between Open Logic Programming (OLP) and Description Logics (DL). A description logic is designed to represent two diierent forms of knowledge. A T-Box represents deenitional knowledge, i.e. deenitions for a set of concepts. An A-Box represents assertional knowledge about speciic domain objects. OLP is a declarative, terminological interpretation of the formalism of Abductive Logic Programming. In this interpretation, an abductive logic program is considered to consist of a T-Box providing deenitions for non-abducible predicates and an A-Box providing assertional knowledge in the form of rst order logic axioms. We deene a provably correct mapping of DL theories to open logic programs, and identify sublanguages of OLP corresponding to several description logics. We also show strong correspondences between derivations produced by a typical DL algorithm and an abductive resolution procedure. The correspondences clarify long-questioned relationships between Logic Programming and Description Logics. To the LP community they may ooer the possibility to import eecient reasoning techniques used in description logics. More importantly, the correspondences indicate the value of OLP as a suitable and highly expressive knowledge representation language, as opposed to both standard LP and rst order logic. As current description logics are all subsets of OLP, the latter may also indicate directions for enhancing the expressivity of the former.