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

@article{Reynolds1992AnAF,
  title={An axiomatization for until and since over the reals without the IRR rule},
  author={Mark Reynolds},
  journal={Studia Logica},
  year={1992},
  volume={51},
  pages={165-193}
}
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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