Notre Dame Journal of Formal Logic

Substructural Fuzzy-Relevance Logic

Eunsuk Yang

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This paper proposes a new topic in substructural logic for use in research joining the fields of relevance and fuzzy logics. For this, we consider old and new relevance principles. We first introduce fuzzy systems satisfying an old relevance principle, that is, Dunn’s weak relevance principle. We present ways to obtain relevant companions of the weakening-free uninorm (based) systems introduced by Metcalfe and Montagna and fuzzy companions of the system R of relevant implication (without distributivity) and its neighbors. The algebraic structures corresponding to the systems are then defined, and completeness results are provided. We next consider fuzzy systems satisfying new relevance principles introduced by Yang. We show that the weakening-free uninorm (based) systems and some extensions and neighbors of R satisfy the new relevance principles.

Article information

Notre Dame J. Formal Logic, Volume 56, Number 3 (2015), 471-491.

Received: 11 December 2010
Accepted: 13 May 2013
First available in Project Euclid: 22 July 2015

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 02C
Secondary: 02J

(substructural) fuzzy-relevance logic fuzzy logic relevance logic uninorm (based) logic


Yang, Eunsuk. Substructural Fuzzy-Relevance Logic. Notre Dame J. Formal Logic 56 (2015), no. 3, 471--491. doi:10.1215/00294527-3132824.

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