Abstract
In this paper, we present an interval tense logic with the inclusion modality, together with the precedence modality. We show that our interval tense logics are decidable. We also investigate the fundamental features of logic to represent realistic temporal intervals, and among them we propose the notion of embeddability of a frame into the time axis, by which all the intervals are mapped into the time axis. Although the class of embeddable frames is not modally definable, we show a decision procedure whether given finite frames are embeddable.
