Composing Complete and Partial Knowledge

We study theory revision and composition in the context of OLPFOL logic. In this logic, the representation of knowledge is split into two parts: writing definitions for completely known concepts (OLP part), and writing constraints and expressing partial knowledge on other concepts (FOL part). In a previous work, the composition of two OLP-FOL theories with nonintersecting sets of defined predicate symbols was studied. It was argued that the composition is given by the set of common models. Here, we consider the case of two OLP-FOL theories, defining the same predicate p and introducing a form of theory revision that makes possible their composition in the sense previously proposed. We introduce two operators for theory revision: the p-opening operator and the conditional p-opening operator. After applying one of these operators to both theories, the knowledge they represent about p is not complete anymore, and the theories can (under certain conditions) be composed.