Intensional First-Order Logic for P2P Database Systems

The meaning of concepts and views defined over a database ontology can be considered as intensional objects which have a particular extension in a given possible world: for instance in the actual world. Thus, non invasive mapping between completely independent peer databases in a P2P systems can be naturally specified by the set of couples of views, which have the same meaning (intension), over two different peers. Such a kind of mapping has very different semantics from standard view-based mappings based on material implication, commonly used for Data Integration Systems. The introduction of an intensional equivalence generates the quotient intensional FOL fundamental for a query answering in P2P systems. In this paper we introduce this formal intensional FOL by fusing Bealer’s intensional algebraic FOL with a possible-world semantics of the Montague’s FOL modal approach to natural language. We modify the Bealer’s intensional algebra in order to deal with relational databases and views, by introducing the join operation of relational algebra. Then we adopt the S5 Kripke frame in order to define an intensional equivalence relation between views for peer databases. Finally, we define an embedding of P2P database system into this quotient intensional FOL, and the computing of its extensionalization mapping in the actual Montague’s world.