Notre Dame Journal of Formal Logic

A Natural Deduction System for First Degree Entailment

Allard M. Tamminga and Koji Tanaka


This paper is concerned with a natural deduction system for First Degree Entailment (FDE). First, we exhibit a brief history of FDE and of combined systems whose underlying idea is used in developing the natural deduction system. Then, after presenting the language and a semantics of FDE, we develop a natural deduction system for FDE. We then prove soundness and completeness of the system with respect to the semantics. The system neatly represents the four-valued semantics for FDE.

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Notre Dame J. Formal Logic Volume 40, Number 2 (1999), 258-272.

First available: 3 December 2002

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Zentralblatt MATH identifier

Primary: 03B47: Substructural logics (including relevance, entailment, linear logic, Lambek calculus, BCK and BCI logics) {For proof-theoretic aspects see 03F52}


Tamminga, Allard M.; Tanaka, Koji. A Natural Deduction System for First Degree Entailment. Notre Dame Journal of Formal Logic 40 (1999), no. 2, 258--272. doi:10.1305/ndjfl/1038949541.

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