Dip. Di Matematica Applicata Ed Informatica Technical Report Series on Computer Science Composing Complete and Partial Knowledge Composing Complete and Partial Knowledge

The representation of knowledge in the logic OLP-FOL 8], 7], is split in two parts: writing deenitions for known concepts, and writing constraints, expressing partial knowledge on other concepts. This is reeected in an OLP-FOL theory T , which is a pair: T = (T d ; T c). The deenition part T d contains the deenitions for known predicates in the form of a normal open logic program (OLP), whereas the rst order logic (FOL) part T c is a set of FOL axioms, expressing partial knowledge on other predicates. The semantics of OLP-FOL is a generalisation of the well-founded semantics 16]. An OLP-FOL theory T = (T d ; T c), divides the set of predicate symbols in two disjoint subsets: the deened predicates, which occur in the head of a clause of T d , and the open predicates, which occur at the most in the body of the clauses of T d. In previous work 17], the composition of two OLP-FOL theories, with non-intersecting sets of deened predicate symbols, was studied. It was argued that their composition is given by the set of common models. Here, we investigate the possibility of composing two OLP-FOL theories, which deene the same predicate. Therefore, we introduce two operators on theories: the p-opening operator, which opens the deenition of the predicate p in a theory completely, and the conditional p-opening operator, which maintains the deenition of p in a theory if a certain condition holds, and opens p in the other cases. We show that we can compose two theories, which both have an open deenition for the same predicate, or which both have a conditional open deenition for the same predicate, with non-overlapping conditions.