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Contemporary use of the term 'Intension' derives from the traditional logical doctrine that an idea has both an extension and an intension. In this paper the authors introduce an intensional FOL (First-Order-Logic) for P2P systems by fusing the Bealer's intensional algebraic FOL with the S5 possible-world semantics of the Montague, they define the intensional equivalence relation for this logic and the weak deductive inference for it. The notion of ontology has become widespread in semantic Web. The meaning of concepts and views defined over some database ontology can be considered as intensional objects which have particular extension in some possible world: for instance in the actual world.
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