Composing Complete and Partial Knowledge

Abstract

The representation of knowledge in the logic OLP-FOL [8], [7], is split in two parts: writing definitions for known concepts, and writing constraints, expressing partial knowledge on other concepts. This is reflected in an OLP-FOL theory T , which is a pair: T = (T d ; T c ). The definition part T d contains the definitions for known predicates in the form of a normal open logic program (OLP), whereas the first 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 defined 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 [19], the composition of two OLP-FOL theories, with non-intersecting sets of defined 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 define the same predicate. Therefore, we introduce two operators on theories: the p-opening operator, which opens the definition of the predicate p in a theory completely, and the conditional p-opening operator, which maintains the definition 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 definition for the same predicate, or which both have a conditional open definition for the same predicate, with non-overlapping conditions