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Axioms for real-time logics

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MPI-I-1999-3-005.pdf
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Citation

Henzinger, T. A., Raskin, J.-F., & Schobbens, P.-Y.(1999). Axioms for real-time logics (MPI-I-1999-3-005). Saarbrücken: Max-Planck-Institut für Informatik.


Cite as: https://hdl.handle.net/11858/00-001M-0000-0014-6F3B-7
Abstract
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 translating $\MITL$ 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 these logics, such as the linear temporal logic of the real numbers (\LTR).