Optimal tableaux for Right Propositional Neighborhood Logic over Linear Orders

The study of interval temporal logics on linear orders is a meaningful research area in computer science and artificial intelligence. Unfortunately, even when restricted to propositional languages, most interval logics turn out to be undecidable. Decidability has been usually recovered by imposing severe syntactic and/or semantic restrictions. In the last years, tableau-based decision procedures have been obtained for logics of the temporal neighborhood and logics of the subinterval relation over specific classes of temporal structures. In this paper, we develop an optimal NEXPTIME tableau-based decision procedure for the future fragment of Propositional Neighborhood Logic over the whole class of linearly ordered domains.