A Modal Logic Formalism for Distributed and Parallel Knowledge Bases

Knowledge bases are currently being investigated by database researchers in order to extend the expressiveness of the relational model to include deductive capabilities in the form of rules. The motivation behind this paper is to present a formalism which extends the relational approach to homogeneous distributed databases to the knowledge base paradigm. The basis of our formalism of distributed knowledge bases is the S5 modal logic system. We define an extensional distributed database as a modal structure and an intentional distributed database as a DatalogK logic program. We interpret a modal structure, (W, V), as a network of user sites, W, together with a valuation function, V, which assigns a database to each site w ∈ W. DatalogK extends Datalog + negation by incorporating into it the modal knowledge operator, K. Knowing in our context can be viewed as data replication, and possibility can be viewed as data fragmentation. We define the model-theoretic semantics of DatalogK via implication in a proper subset of first-order modal logic and its operational semantics in terms of two inflationary fixpoint operators, the local fixpoint and the global fixpoint operators. It is shown that the operational semantics of DatalogK coincides with its model-theoretic semantics and that DatalogK queries are computable in polynomial time. We also demonstrate that DatalogK can be implemented in a parallel knowledge base environment over a shared-nothing architecture for a multiprocessor database.