Sequent calculi for visser’s propositional logics

Katsumasa Ishii; Ryo Kashima; Kentaro Kikuchi

doi:10.1305/ndjfl/1054301352

Sequent calculi for visser’s propositional logics

Katsumasa Ishii, Ryo Kashima, Kentaro Kikuchi

Research output: Contribution to journal › Article › peer-review

8 Citations (Scopus)

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.

Original language	English
Pages (from-to)	1-22
Number of pages	22
Journal	Notre Dame Journal of Formal Logic
Volume	42
Issue number	1
DOIs	https://doi.org/10.1305/ndjfl/1054301352
Publication status	Published - 2001
Externally published	Yes

Keywords

Cut-elimination
Kripke semantics
Sequent calculus

ASJC Scopus subject areas

Logic

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10.1305/ndjfl/1054301352

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abstract = "This paper introduces sequent systems for Visser{\textquoteright}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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AB - 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.

KW - Cut-elimination

KW - Kripke semantics

KW - Sequent calculus

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Sequent calculi for visser’s propositional logics

Abstract

Keywords

ASJC Scopus subject areas

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