Expressive Completeness for Metric Temporal Logic - ULB
Expressive Completeness for Metric Temporal Logic Paul Hunter, Jo¨el Ouaknine, and James Worrell Department of Computer Science University of Oxford United Kingdom OX1 3QD {paul.hunter,joel.ouaknine,james.worrell}@cs.ox.ac.uk
Abstract—Metric Temporal Logic (MTL) is a generalisation of Linear Temporal Logic in which the Until and Since modalities are annotated with intervals that express metric constraints. A result of Hirshfeld and Rabinovich shows that over the reals, first-order logic with binary order relation < and unary function +1 is strictly more expressive than MTL with integervalued constants. Indeed they show that no temporal logic whose modalities are definable by formulas of bounded quantifier depth can be expressively complete for FO(
Abstract—Metric Temporal Logic (MTL) is a generalisation of Linear Temporal Logic in which the Until and Since modalities are annotated with intervals that express metric constraints. A result of Hirshfeld and Rabinovich shows that over the reals, first-order logic with binary order relation < and unary function +1 is strictly more expressive than MTL with integervalued constants. Indeed they show that no temporal logic whose modalities are definable by formulas of bounded quantifier depth can be expressively complete for FO(
