An axiomatization for until and since over the reals without the IRR rule

Studia Logica 51 (2):165 - 193 (1992)
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Abstract

We give a Hilbert style axiomatization for the set of formulas in the temporal language with Until and Since which are valid over the real number flow of time. The axiomatization, which is orthodox in the sense of only having the usual temporal rules of inference, is complete with respect to single formulas.

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Citations of this work

Adding a temporal dimension to a logic system.Marcelo Finger & Dov M. Gabbay - 1992 - Journal of Logic, Language and Information 1 (3):203-233.
Derivation rules as anti-axioms in modal logic.Yde Venema - 1993 - Journal of Symbolic Logic 58 (3):1003-1034.
Adding a temporal dimension to a logic system.Dov M. Gabbay & Marcelo Finger - 1992 - Journal of Logic, Language and Information 1 (3):203-233.
Combining Temporal Logic Systems.Marcelo Finger & Dov Gabbay - 1996 - Notre Dame Journal of Formal Logic 37 (2):204-232.
The complexity of temporal logic over the reals.Mark Reynolds - 2010 - Annals of Pure and Applied Logic 161 (8):1063-1096.

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References found in this work

Axioms for tense logic. I. "Since" and "until".John P. Burgess - 1982 - Notre Dame Journal of Formal Logic 23 (4):367-374.
The decision problem for linear temporal logic.John P. Burgess & Yuri Gurevich - 1985 - Notre Dame Journal of Formal Logic 26 (2):115-128.
A complete deductive-system for since-until branching-time logic.Alberto Zanardo - 1991 - Journal of Philosophical Logic 20 (2):131 - 148.
Linear Orderings.Joseph G. Rosenstein - 1983 - Journal of Symbolic Logic 48 (4):1207-1209.

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