## Notre Dame Journal of Formal Logic

### Substructural Fuzzy-Relevance Logic

Eunsuk Yang

#### Abstract

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

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

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

Permanent link to this document
https://projecteuclid.org/euclid.ndjfl/1437570857

Digital Object Identifier
doi:10.1215/00294527-3132824

Mathematical Reviews number (MathSciNet)
MR3373615

Zentralblatt MATH identifier
1334.03030

Subjects
Primary: 02C
Secondary: 02J

#### Citation

Yang, Eunsuk. Substructural Fuzzy-Relevance Logic. Notre Dame J. Formal Logic 56 (2015), no. 3, 471--491. doi:10.1215/00294527-3132824. https://projecteuclid.org/euclid.ndjfl/1437570857

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