PROPOSITIONAL MODAL LOGIC OF TIME INTERVALS.

Abstract

In certain areas of artificial intelligence there is need to represent continuous change and to make statements that are interpreted with respect to time intervals rather than time points. To this end the authors develop a modal temporal logic based on time intervals, a logic that can be viewed as a generalization of point-based modal temporal logic. They discuss related logics, give an intuitive presentation of the new logic, and define its formal syntax and semantics. The underlying nature of time is allowed to be discrete or continuous, and linear or branching, complete (such as the reals) or not. However, it is shown that there are formulas in the logic that allow all these situations to be distinguished. A translation of the modal logic into first-order logic is shown which allows some results on first-order logic to be applied. The difficulty of the validity problem for the logic is considered.