Basic substructural core fuzzy logics and their extensions: Mianorm-based logics

Yang, Eunsuk

doi:10.1016/j.fss.2015.09.007

Cited by 10 publications

(4 citation statements)

References 22 publications

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“…In this paper, we prove that UL ω and IUL ω are standard complete by Wang's constructions in [5] and [6], which are some generalizations of the Jenei and Montagna-style approach for proving standard completeness for monoidal t-norm-based logic MTL [7] and the proof of the standard completeness for IMTL given by Esteva, Gispert, Godo, and Montagna in [8]. These constructions have been extended by Yang in [9][10][11][12].…”

Section: Introductionmentioning

confidence: 87%

Logics for Finite UL and IUL-Algebras Are Substructural Fuzzy Logics

Wang

2018

Symmetry

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Section: Introductionmentioning

confidence: 87%

Logics for Finite UL and IUL-Algebras Are Substructural Fuzzy Logics

Wang

2018

Symmetry

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“…Here we recall the most basic substructural core fuzzy logic MIAL and its axiomatic extensions (extensions for short) and their algebraic semantics (See [42] for more detailed introduction of these logics and semantics). The language for these logics is provided over a countable propositional language with Fm (a set of formulas) built from VAR (a set of propositional variables), propositional constants t, f , F, T, and connectives →, , ∧, ∨, &.…”

Section: Algebraic Semantics For Basic Core Fuzzy Logicsmentioning

confidence: 99%

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

Yang

2021

Axioms

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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.

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“…But these approaches do not work for UML (= C 2 UL) and IUML (= C 2 IUL with FP). (For the similarities and differences between constructions of Yang and Wang's Jenei-Montagna-style, see Reference [29]).…”

Section: Introductionmentioning

confidence: 99%

“…For convenience, we adopted notations and terminology similar to those in References [9,22,[29][30][31][32][33], and we assume reader familiarity with them (together with results found therein). ¬ϕ := ϕ → f, and df2.…”

Section: Introductionmentioning

confidence: 99%

Fixpointed Idempotent Uninorm (Based) Logics

Yang

2019

Mathematics

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Idempotent uninorms are simply defined by fixpointed negations. These uninorms, called here fixpointed idempotent uninorms, have been extensively studied because of their simplicity, whereas logics characterizing such uninorms have not. Recently, fixpointed uninorm mingle logic (fUML) was introduced, and its standard completeness, i.e., completeness on real unit interval [ 0 , 1 ] , was proved by Baldi and Ciabattoni. However, their proof is not algebraic and does not shed any light on the algebraic feature by which an idempotent uninorm is characterized, using operations defined by a fixpointed negation. To shed a light on this feature, this paper algebraically investigates logics based on fixpointed idempotent uninorms. First, several such logics are introduced as axiomatic extensions of uninorm mingle logic (UML). The algebraic structures corresponding to the systems are then defined, and the results of the associated algebraic completeness are provided. Next, standard completeness is established for the systems using an Esteva–Godo-style approach for proving standard completeness.

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Basic substructural core fuzzy logics and their extensions: Mianorm-based logics

Cited by 10 publications

References 22 publications

Logics for Finite UL and IUL-Algebras Are Substructural Fuzzy Logics

Logics for Finite UL and IUL-Algebras Are Substructural Fuzzy Logics

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

Fixpointed Idempotent Uninorm (Based) Logics

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