On the Decidability and Complexity of Some Fragments of Metric Temporal Logic

Abstract

Metric Temporal Logic, MTL pw [UI , SI ], is amongst the most studied real-time logics. It exhibits considerable diversity in expressiveness and decidability properties based on the permitted set of modalities and the nature of time interval constraints I. In this paper, we sharpen the decidability results by showing that the satisfiability of MTL pw [ UI , SNS] (where N S denotes non-singular intervals) is also decidable over finite pointwise strictly monotonic time. We give a satisfiability preserving reduction from MTL pw [ UI , SNS] to the decidable logic MTL pw [ UI ] of Ouaknine and Worrell using a novel technique of temporal projections with oversampling. We also investigate the decidability of unary fragment MTL pw [♦I , ♦− I ] and we compare the expressive powers of some of these fragments.