Notre Dame Journal of Formal Logic

Sequent Calculi for Visser's Propositional Logics

Katsumasa Ishii, Ryo Kashima, and Kentaro Kikuchi


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.

Article information

Notre Dame J. Formal Logic, Volume 42, Number 1 (2001), 1-22.

First available in Project Euclid: 30 May 2003

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 03F05: Cut-elimination and normal-form theorems
Secondary: 03B60: Other nonclassical logic

sequent calculus Kripke semantics cut-elimination


Ishii, Katsumasa; Kashima, Ryo; Kikuchi, Kentaro. Sequent Calculi for Visser's Propositional Logics. Notre Dame J. Formal Logic 42 (2001), no. 1, 1--22. doi:10.1305/ndjfl/1054301352.

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