Interleaving set temporal logic

Abstract

A new temporal logic and interpretation are suggested which have features from linear temporal logic, branching time temporal logic, and partial order temporal logic. The new logic can describe properties essential to the specification and correctness proofs of distributed algorithms, such as those for global snapshots. It is also appropriate for the justification of proof rules and for ascribing temporal semantics to properties such as layering of a program. These properties cannot be described with existing temporal logics. The semantic model of the logic is based on a collection of sets of interleaving sequences which reflect partial orders from the underlying semantics of the computational model. For the common partial order derived from sequentiality in execution of each process, the logic will distinguish between nondeterminism due to the parallel execution and nondeterminism due to local nondeterministic choices. The difference in expressive power is thus qualitative, and not merely due to the presence or absence of a particular temporal operator. In the logic, theorems are proven which clarify when it is possible to establish a property P for some of the interleaving computations, and yet conclude the truth of P for every interleaving.