A natural deduction system for first degree entailment

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Notre Dame Journal of Formal Logic 40 (2):258-272 (1999)
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Abstract

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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10.1305/ndjfl/1038949541

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Author Profiles

Photo of Allard Tamminga
Allard Tamminga
University of Greifswald
Photo of Koji Tanaka
Koji Tanaka
Australian National University

Citations of this work

Unified Natural Deduction for Logics of Strong Negation.Norihiro Kamide & Sara Negri - 2025 - Notre Dame Journal of Formal Logic 66 (4):543-580.
Dialectical Dispositions and Logic.Lionel Shapiro - 2025 - In Igor Sedlar, The Logica Yearbook 2023. College Publications.

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References found in this work

First-order logic.Raymond Merrill Smullyan - 1968 - New York [etc.]: Springer Verlag.
Entailment: The Logic of Relevance and Necessity. - 1975 - Studia Logica 54 (2):261-266.
Paraconsistent logic.Graham Priest - 2008 - Stanford Encyclopedia of Philosophy.
Basic proof theory.A. S. Troelstra - 1996 - New York: Cambridge University Press. Edited by Helmut Schwichtenberg.

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