A four-valued semantics for terminological logics (Q1115428)

A certain formal semantics for terminological logics formalizing the notion of frames is proposed. The four-valued semantics considered here includes the possibility to have inconsistent knowledge about some proposition without being totally inconsistent. A detailed discussion concerning the proposed semantics is given in the fourth section of the paper. For concepts and roles in canonical form, Theorem 1 in the fifth section gives a sound and complete characterization of subsumption. Next, an algorithm for subsumption for canonical form concepts and roles is derived from the given characterization. Technical results, mainly the proofs of the asserted properties as soundness and completeness corresponding to the proposed algorithm, are given in Appendix A.