Jean-Francois Raskin, Pierre-Yves Schobbens, and Thomas A. Henzinger
This paper presents a complete axiomatization of two decidable propositional real-time linear temporal logics: Event Clock Logic (ECL) and Metric Interval Temporal Logic with past (MITL). The completeness proof consists of an effective proof building procedure for ECL. From this result we obtain a complete axiomatization of MITL by providing axioms translating MITL formulae into ECL formulae, the two logics being equally expressive. Our proof is structured to yield axiomatizations also for interesting fragments of these logics, such as the linear temporal logic of the real numbers (LTR).
Theoretical Computer Science 274:151-182, 2002. A preliminary version appeared in the Proceedings of the Ninth International Conference on Concurrency Theory (CONCUR), Lecture Notes in Computer Science 1466, Springer, 1998, pp. 219-236.