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

Metric Temporal Logic, MTL[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 [ UI , SNS] (where NS denotes non-singular intervals) is also decidable over finite pointwise strictly monotonic time. We give a satisfiability preserving reduction from MTL[ UI , SNS ] to the decidable logic MTL [ UI ] of Ouaknine and Worrell using a novel technique of temporal projections with oversampling. We also investigate the decidability of unary fragment MTL[♦I ,♦ −I ] and we compare the expressive powers of some of these fragments.