Many-dimensional Modal Logic of Tense and Temporal Interval and its Decidability

Linear tense logics are widely accepted for structural temporal representation, where the basic has two modal operators G and H, each of which represents the future and the past, respectively. On the other hand, the temporal interval relations arranged by Allen have long been the standard of natural language semantics, though it still lacks the modal-logical foundation. Van Benthem [10] proposed and in regard to the accessibility to overlapping intervals and subintervals, respectively; however, the logical feature of the modality has not well studied. In this study, we propose a manydimensional logic including the conventional tense logic, together with such interval accessibility, and show its decidability. Keywords— decidability, many-dimensional modal logic, sequent system, temporal logic.