First Steps towards Automated Synthesis of Tableau Systems for Interval Temporal Logics

Interval temporal logics are difficult to deal with in many respects. In the last years, various meaningful fragments of Halpern and Shoham’s modal logic of time intervals have been shown to be decidable with complexities that range from NP-complete to non-primitive recursive. However, even restricting the attention to finite interval structures, the step from modeltheoretic decidability results to the actual implementations of tableau-based decision procedures is quite challenging. In this paper, we investigate the possibility of making use of automated tableau generators. More precisely, we exploit the generator METTEL2 to implement a tableau-based decision procedure for the future fragment of the logic of temporal neighborhood over finite linear orders. We explore and contrast two alternative solutions: a concrete tableau system, that operates on a concrete interval structure explicitly built over a finite, linearly-ordered set of points, and an abstract one, that operates on an interval frame which is forced to be isomorphic to a concrete interval structure by suitably constraining its accessibility relation. Keywords–Interval temporal logics; satisfiability; tableaux; automated tableau generation.