Sequent Calculi for Visser's Propositional Logics

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Notre Dame Journal of Formal Logic 42 (1):1-22 (2001)
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Abstract

This paper introduces sequent systems for Visser's two propositional logics: Basic Propositional Logic (BPL) and Formal Propositional Logic (FPL). It is shown through semantical completeness that the cut rule is admissible in each system. The relationships with Hilbert-style axiomatizations and with other sequent formulations are discussed. The cut-elimination theorems are also demonstrated by syntactical methods.

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10.1305/euclid.ndjfl/1054301352

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Citations of this work

Sequent Calculi for Orthologic with Strict Implication.Tomoaki Kawano - 2022 - Bulletin of the Section of Logic 51 (1):73-89.
A cut-free Gentzen formulation of basic propositional calculus.Kentaro Kikuchi & Katsumi Sasaki - 2003 - Journal of Logic, Language and Information 12 (2):213-225.
New sequent calculi for Visser's Formal Propositional Logic.Katsumasa Ishii - 2003 - Mathematical Logic Quarterly 49 (5):525.

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References found in this work

Basic Propositional Calculus I.Mohamed Ardeshir & Wim Ruitenberg - 1998 - Mathematical Logic Quarterly 44 (3):317-343.
Speaking about transitive frames in propositional languages.Yasuhito Suzuki, Frank Wolter & Michael Zakharyaschev - 1998 - Journal of Logic, Language and Information 7 (3):317-339.
Basic Predicate Calculus.Wim Ruitenburg - 1998 - Notre Dame Journal of Formal Logic 39 (1):18-46.
The modal logic of provability: Cut-elimination. [REVIEW]Silvio Valentini - 1983 - Journal of Philosophical Logic 12 (4):471 - 476.

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