The notion of ontology has become widespread in fields such as intelligent information integration, information retrieval, electronic commerce and semantic Web. We consider the incomplete nature of the information in Web, so that each ontology of a peer is a logic theory of a database with a more than one minimal Herbrand model. Because of that the contributions to the query answer of any peer are given by the known answers only (which are true in all models of a peer-database) that such peer provides. The semantics of view-based mappings between peer ontologies has to be based only on known answers from peers, so that these mappings, in a Gabbay-style rules, need a Hybrid modal logic language or, alternatively, multi-modal logic, to be correctly specified. We show that the query answers for local peer databases are computed according to the epistemic modal S5 logic, where frames are partitioned according to the structure of peers. But also the global P2P query answering is based on a modal logic and we define it formally. Finally, we present coalgebraic semantics for such P2P database systems, and for a grid-computing query processing system.
展开▼
