Axiomatizations of Interval Logics

Abstract

Interval logic has been introduced as a temporal logic that provides higher-level constructs and an intuitive graphical representation, making it easier in interval logic than in other temporal logics to specify and reason about concurrency in software and hardware designs. In this paper we present axiomatizations for two propositional interval logics and relate these logics to Until Temporal Logic. All of these logics are discrete linear-time temporal logics with no next operator. The next operator obstructs the use of hierarchical abstraction and refinement, and makes reasoning about concurrency difficult. 1 Introduction Although temporal logic has been widely recognized as an appropriate logic for reasoning about the relative ordering of events in concurrent systems, ordinary programmers and system designers have found temporal logic unintuitive and difficult to use. The difficulty stems mainly from the need to establish temporal contexts within which requirements apply. Interval ..