Incompleteness of First-Order Temporal Logic with Until

@article{Szalas1988IncompletenessOF,
  title={Incompleteness of First-Order Temporal Logic with Until},
  author={Andrzej Szalas and Leszek Holenderski},
  journal={Theor. Comput. Sci.},
  year={1988},
  volume={57},
  pages={317-325}
}
The results presented in this paper concern the axiomatizability problem of first-order temporal logic with linear and discrete time. We show that the logic is incomplete, i.e., it cannot be provided with a finitistic and complete proof system. We show two incompleteness theorems. Although the first one is weaker (it assumes some first-order signature), we decided to present it, for its proof is much simpler and contains an interesting fact that finite sets are characterizable by means of… CONTINUE READING

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Pnueli , Verification of concurrent programs : the temporal framework

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