Revisiting MITL to Fix Decision Procedures

Abstract

Metric Interval Temporal Logic ( MITL ) is a well studied real-time, temporal logic that has decidable satisfiability and model checking problems. The decision procedures for MITLrely on the automata theoretic approach, where logic formulas are translated into equivalent timed automata. Since timed automata are not closed under complementation, decision procedures for MITLfirst convert a formula into negated normal form before translating to a timed automaton. We show that, unfortunately, these 20-year-old procedures are incorrect, because they rely on an incorrect semantics of the \(\mathcal {R}\) operator. We present the right semantics of \(\mathcal {R}\) and give new, correct decision procedures for MITL. We show that both satisfiability and model checking for MITLare Open image in new window , as was previously claimed. We also identify a fragment of MITLthat we call MITL WIthat is richer than \(\texttt {MITL}_{0,\!\infty }\), for which we show that both satisfiability and model checking are Open image in new window . Many of our results have been formally proved in PVS