DFC-algorithms for Suszko logic and one-to-one Gentzen type formalizations

✍ Scribed by Anita Wasilewska

• Book ID: 104744954
• Publisher: Springer Netherlands
• Year: 1984
• Tongue: English
• Weight: 554 KB
• Volume: 43
• Category: Article
• ISSN: 0039-3215
• DOI: 10.1007/bf00370509

✦ Synopsis

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 r 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).

1. Finite control deterministic algorithms and languages associated with

them.