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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The author would like to thank Dov Gabbay, Yde Venema, the referee and especially Ian Hodkinson for helpful comments during the development of this work. The work was supported by the U.K. Science and Engineering Research Council under the Metatem project (GR/F/28526).
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Reynolds, M. An axiomatization for until and since over the reals without the IRR rule. Stud Logica 51, 165–193 (1992). https://doi.org/10.1007/BF00370112
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DOI: https://doi.org/10.1007/BF00370112