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DFC-Algorithms for Suszko Logic and One-to-One Gentzen Type Formalizations

Anita Wasilewska
Studia Logica: An International Journal for Symbolic Logic
Vol. 43, No. 4 (1984), pp. 395-404
Published by: Springer
Stable URL: http://www.jstor.org/stable/20015186
Page Count: 10
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DFC-Algorithms for Suszko Logic and One-to-One Gentzen Type Formalizations
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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 propositional 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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