A Tableau-Based Decision Procedure for Right Propositional Neighborhood Logic

Abstract

Propositional interval temporal logics are quite expressive temporal logics that allow one to naturally express statements that refer to time intervals. Unfortunately, most such logics turned out to be (highly) undecidable. To get decidability, severe syntactic and/or semantic restrictions have been imposed to interval-based temporal logics that make it possible to reduce them to point-based ones. The problem of identifying expressive enough, yet decidable, new interval logics or fragments of existing ones which are genuinely interval-based is still largely unexplored. In this paper, we make one step in this direction by devising an original tableau-based decision procedure for the future fragment of Propositional Neighborhood Interval Temporal Logic, interpreted over natural numbers.