Basic Core Fuzzy Logics and Algebraic Routley–Meyer-Style Semantics

Abstract

Recently, algebraic Routley–Meyer-style semantics was introduced for basic substructural logics. This paper extends it to fuzzy logics. First, we recall the basic substructural core fuzzy logic MIAL (Mianorm logic) and its axiomatic extensions, together with their algebraic semantics. Next, we introduce two kinds of ternary relational semantics, called here linear Urquhart-style and Fine-style Routley–Meyer semantics, for them as algebraic Routley–Meyer-style semantics.

Keywords

• operational semantics
• Routley–Meyer-style semantics
• algebraic semantics
• (core) fuzzy logics
• implicational tonoid fuzzy logics