# Temporal logic programming with metric and past operators

## Abstract

Temporal logic allows us to use logic programming to specify and to program dynamically changing situations and non-terminating computations in a natural and problem oriented way. Recently so called metric or real-time temporal logics have been proposed for the specification of real-time systems, for which not only qualitative but also quantitative temporal properties are very important. In this work we investigate a subset of metric temporal Horn logic called *MTL-programs*, for which we give a translation into CLP(*A*′)-programs and CLP(*A*′)-goals over a suitable algebra *A*′. We give a restriction of the CLP(*A*′)-derivation mechanism sufficient for the derivation of MTL-goals from MTL-programs, which admits efficient satisfiability checking of the constraints generated. Its worst case complexity is linear in the number of variables involved, contrary to general satisfiability checking of constraints over *A*′ which is NP-complete. Moreover, we show that an extension of the metric temporal logic considered by the inclusion of variables within the temporal operators leads already to a temporal Horn logic which is expressively equivalent to constraint logic programs over *A*′.

## Keywords

Logic Program Modal Logic Temporal Logic Logic Programming Past Operator## Preview

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