# A Polynomial Translation of S4 into T and Contraction-Free Tableaux for S4

```@article{Cerrito1997APT,
title={A Polynomial Translation of S4 into T and Contraction-Free Tableaux for S4},
author={Serenella Cerrito and Marta Cialdea Mayer},
journal={Log. J. IGPL},
year={1997},
volume={5},
pages={287-300}
}```
• Published 1 March 1997
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The concern of this paper is the study of automated deduction methods for propositional modal logics. We use tableau proof-systems to show that Fitting's translation of the transitive modal logic S4 into T can be constructed in deterministic polynomial time. This result is exploited in order to establish a polynomial bound to the length of branches in both tableau and sequent proof search for the transitive logics S4 and K4. This allows the elimination of \periodicity tests" when proving S4…
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