Description Logic Programs: A Paraconsistent Relational Model Approach

A description logic program (dl-program) consists of a description logic knowledge base (a terminological box and an assertion box) and a set of rules for a logic program. For such description logic programs, instead of providing the fixed-point semantics for dl-programs by the immediate consequence operator, we propose an algorithm based on the paraconsistent relational model that mimics the immediate consequence operator of dl-programs. We also introduce a dl-paraconsistent relation (dl-relation), which is essential for sending information between description logic and logic programs represented in terms of equations containing paraconsistent relations. The first step in our algorithm is to convert rules, which may contain dl-atoms that enable the flow of information between description logic and logic programs, into paraconsistent relation equations that contain paraconsistent relational algebraic operators. The second step is to determine iteratively the fixed-point semantics for dl-programs using these equations. We will also prove the correctness of both steps of the algorithm.