Towards a Theory of Frames and Rules

A term definition language very similar to the terminological part of BACK is enriched with horn-like rules and disjointness restrictions built up from arbitrary concepts possibly involving syntactic or semantic cycles. The resulting hybrid language is given a weak semantics which captures the inferences expected intuitively and allows for representing some kind of procedural knowledge. The weak semantics used is based on model theoretic grounds and, even more important, allows to prove properties of the language very easily. Moreover an algorithm is developed which is sound and and complete with respect to the weak semantics and can be characterized to be polynomially time bound for non-pathological cases.