Knowledge and the Logic of Local Propositions

An agent's limited view of the state of a distributed system may render globally diierent situations indistinguishable. A proposition is local for this agent whenever his view suuces to decide this proposition. Motivated by a framework for the development of distributed programs from knowledge-based speciications, we introduce a modal logic of local propositions , in which it is possible to quantify over such propositions. We show that this logic is able to represent a rich set of epistemic notions. Under the usual strong semantics, this logic is not recursively axiomatizable, however. We show that by weakening the semantics of quantiication, it is possible to obtain a logic that is axiomatizable and is still able to express interesting epistemic notions.