This paper presents a complete axiomatization of fully decidable propositional real-time linear temporal logics with past: the Event Clock Logic (ECL) and the 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 that allows the translation of MITL formulae into ECL formulae, the two logics being equally expressive. Our proof is structured to yield a similar axiomatization and procedure for interesting fragments of this logic: the linear temporal logic of the real numbers (LTR), the fragment with only past clocks.
|Title of host publication||CONCUR'98|
|Subtitle of host publication||9th International Conference on Concurrency Theory|
|Editors||D Sangiorgi, R de|
|Publication status||Published - 1998|