Abstract
We use here the notions and results from algebraic theory of programs in order to give a new proof of the decidability theorem for Suszko logic SCI (Theorem 3).
We generalize the method used in the proof of that theorem in order to prove a more general fact that any prepositional logic which admits a cut-free Gentzen type formalization is decidable (Theorem 6).
We establish also the relationship between the Suszko Logic SCI, one-to-one Gentzen type formalizations and deterministic and algorithmic regular languages (Remark 2 and Theorem 7, respectively).
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A. Wasilewska, Programs and logics, to appear in Studia Logica.
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Wasilewska, A. DFC-algorithms for Suszko logic and one-to-one Gentzen type formalizations. Stud Logica 43, 395–404 (1984). https://doi.org/10.1007/BF00370509
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DOI: https://doi.org/10.1007/BF00370509