Paraconsistency, relevance, and vagueness: A proof-theoretic approach to fuzzy relevant logic FR.

Articles in Press

Document Type : Research Paper

Authors

1 Department of Philosophy, Wisdom and Logic, Faculty of Humanities, Tarbiat Modares University, Tehran.Iran

2 Department of Philosophy, Wisdom and Logic, Faculty of Humanities, Tarbiat Modares University, Tehran, Iran

10.22034/jpiut.2026.70950.4391

Abstract

In scientific and even in everyday reasoning, and also in our intuitive understanding, relevance-preserving is of particular importance alongside truth-preserving. In an other hand,, we deal with many reasonings that are approximate and are true to a certain degree. In this article, considering two important categories in natural language and logic, namely "relevance" and "vagueness", with a formal approach, and in continuation of the work of the my MSc's thesis entitled "Fuzzy Relational Logic: A Propositional Approach", we present a Hilbert-style system and a hypersequent calculus as proof theories for fuzzy relevant semantics, and introduce logics are constructed whose reasoning is both fuzzy and relevant, and are called fuzzy relevant logics. Some fuzzy relevant logics (such as FRM) are obtained by eliminating the constants F and T, and some others are obtained without eliminating these constants and by adding the guaranteeing logical rules of prelinearity and excluded middle. In addition to the considerations of proof theory, the metatheorems of these logics will be addressed and the soundness and completeness (or incompleteness) will be proven with respect to ordered linear algebras (matrices). Philosophical considerations based on these proof theories and also the investigation of structural rules for resolving vagueness paradoxes are among the philosophical considerations of this research.

Keywords

Main Subjects

Send comment about this article
CAPTCHA Image
Journal of Philosophical Investigations

Articles in Press, Accepted Manuscript
Available Online from 19 February 2026

Files

Share

How to cite

Statistics