Mixed Propositional Metric Temporal Logic: A New Formalism for Temporal Planning

Temporal logics have been used in autonomous planningto represent and reason about temporal planning problems.However, such techniques have typically been restricted toeither (1) representing actions, events, and goals with temporalproperties or (2) planning for temporally-extended goalsunder restrictive conditions of classical planning. We introduceMixed Propositional Metric Temporal Logic (MPMTL),where formulae in MPMTL are built over mixed binary andcontinuous real variables. MPMTL provides a natural, flexibleformalism for representing and reasoning about temporalproblems. We analyze the complexity of MPMTL formulaesatisfiability and model checking, and identify MPMTLfragments with lower complexity. We also introduce an approachto world modeling using a timeline vector, relevant totemporal planning with continuous change (as opposed to theuse of discrete states). Our model supports retroactive actionprogression, concurrent and overlapping actions with discreteand continuous changes, and concurrent effects to the samevariable. For reasoning about this temporal planning problem,we define a progression function for actions with thenew temporal properties and a solution to this temporal task.