Tiered logic for agents in contexts

We introduce a new kind of logic for agents in different localities, which works in tiers or layers. At the base are local worlds with their own logic. Above them is a global logic that takes statements from the local worlds and combines them. This allows communications between the different localities. We give a basic example using first order logic as the local logic and propositional calculus at the global level. As a more sophisticated example we use the algebraic specification language CASL and take the locations as specifications. Moreover we then permit the combination of such specifications according to the architectural specifications of CASL. Although we only consider two layers in the present paper, we see no reason why the approach should not be extended to any finite number of tiers. We prove soundness and completeness proofs for our logics.