Distributed States Temporal Logic

Abstract

We introduce a temporal logic to reason on global applications in an asynchronous setting. First, we define the Distributed States Logic (DSL), a modal logic for localities that embeds the local theories of each component into a theory of the distributed states of the system. We provide the logic with a sound and complete axiomatization. The contribution is that it is possible to reason about properties that involve several components, even in the absence of a global clock. Then, we define the Distributed States Temporal Logic (DSTL) by introducing temporal operators a' la Unity. We support our proposal by working out a pair of examples: a simple secure communication system, and an algorithm for distributed leader election. The motivation for this work is that the existing logics for distributed systems do not have the right expressive power to reason on the systems behaviour, when the communication is based on asynchronous message passing. On the other side, asynchronous communication is the most used abstraction when modelling global applications.