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.
Highlights
Semantics means semantics with operations in place of binary accessibility relations, the frames of which have the same structures as algebraic semantics.) for substructural fuzzy logics have been introduced extensively, ARM semantics for such logics have not
As in [1], we introduce two kinds of ARMsemantics: one is the semantics with the definition and linearly ordered models, called here linear
We investigated ARM semantics for substructural fuzzy logics based on mianorms
Summary
The more detailed other reasons to study this are as follows: The first and most important reason is that while algebraic Kripke-style (briefly AK) semantics (The term AK semantics means semantics with operations in place of binary accessibility relations, the frames of which have the same structures as algebraic semantics.) for substructural fuzzy logics have been introduced extensively (see, e.g., [17,18,19,20,30,31,32]), ARM semantics for such logics have not. As in [1], our ARM semantics in Sections 3.1 and 3.2 provides frames as some reducts of their corresponding algebras and defines ternary relations using binary operations and (in)equations. By ARMsemantics, we mean this kind of ARM semantics
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