scholarly journals A Proof of the Standard Completeness for the Involutive Uninorm Logic

Symmetry ◽  
2019 ◽  
Vol 11 (4) ◽  
pp. 445 ◽  
Author(s):  
SanMin Wang
Keyword(s):  
Open Problem ◽  
Substructural Logics ◽  
Uniform Method ◽  
Fuzzy Logics ◽  
Standard Completeness

In this paper, we solve a long-standing open problem in the field of fuzzy logics, that is, the standard completeness for the involutive uninorm logic IUL. In fact, we present a uniform method of density elimination for several semilinear substructural logics. Especially, the density elimination for IUL is proved. Then the standard completeness for IUL follows as a lemma by virtue of previous work by Metcalfe and Montagna.

scholarly journals Density Elimination for Semilinear Substructural Logics

2019 ◽  
Author(s):  
SanMin Wang
Keyword(s):  
Substructural Logics ◽  
Uniform Method ◽  
Standard Completeness

We present a uniform method of density elimination for several semilinear substructural logics. Especially, the density elimination for the involutive uninorm logic IUL is proved. Then the standard completeness of IUL follows as a lemma by virtue of previous work by Metcalfe and Montagna.

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

Symmetry ◽  
2018 ◽  
Vol 10 (12) ◽  
pp. 755
Author(s):  
Sanmin Wang
Keyword(s):  
Substructural Logics ◽  
Fuzzy Logics ◽  
Standard Completeness

Semilinear substructural logics UL ω and IUL ω are logics for finite UL and IUL -algebras, respectively. In this paper, the standard completeness of UL ω and IUL ω is proven by the method developed by Jenei, Montagna, Esteva, Gispert, Godo, and Wang. This shows that UL ω and IUL ω are substructural fuzzy logics.

scholarly journals ${\rm {\bf UL}}_\omega $ and ${\rm {\bf IUL}}_\omega $ Are Substructural Fuzzy Logics

2018 ◽  
Author(s):  
SanMin Wang
Keyword(s):  
Substructural Logics ◽  
Fuzzy Logics ◽  
Standard Completeness

Two representable substructural logics ${\rm {\bf UL}}_\omega $ and ${\rm {\bf IUL}}_\omega $ are logics for finite UL and IUL-algebras, respectively. In this paper, the standard completeness of ${\rm {\bf UL}}_\omega $ and ${\rm {\bf IUL}}_\omega $ is proved by the method developed by Jenei, Montagna, Esteva, Gispert, Godo and Wang. This shows that ${\rm {\bf UL}}_\omega $ and ${\rm {\bf IUL}}_\omega $ are substructural fuzzy logics.

SUBSTRUCTURAL INQUISITIVE LOGICS

2019 ◽  
Vol 12 (2) ◽  
pp. 296-330 ◽  
Author(s):  
VÍT PUNČOCHÁŘ
Keyword(s):  
Fuzzy Logic ◽  
General Theory ◽  
Propositional Logic ◽  
Substructural Logics ◽  
Substructural Logic ◽  
Fuzzy Logics ◽  
Inquisitive Semantics ◽  
Semantic Framework ◽  
Noncommutative Version ◽  
Image Position

AbstractThis paper shows that any propositional logic that extends a basic substructural logic BSL (a weak, nondistributive, nonassociative, and noncommutative version of Full Lambek logic with a paraconsistent negation) can be enriched with questions in the style of inquisitive semantics and logic. We introduce a relational semantic framework for substructural logics that enables us to define the notion of an inquisitive extension of λ, denoted as ${\lambda ^?}$, for any logic λ that is at least as strong as BSL. A general theory of these “inquisitive extensions” is worked out. In particular, it is shown how to axiomatize ${\lambda ^?}$, given the axiomatization of λ. Furthermore, the general theory is applied to some prominent logical systems in the class: classical logic Cl, intuitionistic logic Int, and t-norm based fuzzy logics, including for example Łukasiewicz fuzzy logic Ł. For the inquisitive extensions of these logics, axiomatization is provided and a suitable semantics found.

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

Axioms ◽  
2021 ◽  
Vol 10 (4) ◽  
pp. 273
Author(s):  
Eunsuk Yang
Keyword(s):  
Fuzzy Logic ◽  
Substructural Logics ◽  
Algebraic Semantics ◽  
Relational Semantics ◽  
Fuzzy Logics

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.

Strong non-standard completeness for fuzzy logics

2007 ◽  
Vol 12 (4) ◽  
pp. 321-333 ◽  
Author(s):  
Tommaso Flaminio
Keyword(s):  
Fuzzy Logics ◽  
Standard Completeness

Substructural fuzzy logics

2007 ◽  
Vol 72 (3) ◽  
pp. 834-864 ◽  
Author(s):  
George Metcalfe ◽  
Franco Montagna
Keyword(s):  
Linear Logic ◽  
Substructural Logics ◽  
Unit Interval ◽  
Residuated Lattices ◽  
Cut Elimination ◽  
Algebraic Semantics ◽  
Fuzzy Logics ◽  
The Real ◽  
Gentzen Systems ◽  
Intuitionistic Linear Logic

AbstractSubstructural fuzzy logics are substructural logics that are complete with respect to algebras whose lattice reduct is the real unit interval [0, 1]. In this paper, we introduce Uninorm logic UL as Multiplicative additive intuitionistic linear logic MAILL extended with the prelinearity axiom ((A → B) ∧ t) V ((B → A)∧ t). Axiomatic extensions of UL include known fuzzy logics such as Monoidal t-norm logic MIX and Gödel logic G, and new weakening-free logics. Algebraic semantics for these logics are provided by subvarieties of (representable) pointed bounded commutative residuated lattices. Gentzen systems admitting cut-elimination are given in the framework of hypersequents. Completeness with respect to algebras with lattice reduct [0, 1] is established for UL and several extensions using a two-part strategy. First, completeness is proved for the logic extended with Takeuti and Titani's density rule. A syntactic elimination of the rule is then given using a hypersequent calculus. As an algebraic corollary, it follows that certain varieties of residuated lattices are generated by their members with lattice reduct [0, 1].

The Yukawa Potential Function and Reciprocal Univalent Function

2013 ◽  
Vol 3 (2) ◽  
pp. 197-202
Author(s):  
Amir Pishkoo ◽  
Maslina Darus
Keyword(s):  
Mathematical Model ◽  
Unit Disk ◽  
Potential Function ◽  
Univalent Function ◽  
Open Problem ◽  
Yukawa Potential ◽  
Reciprocal Theorem ◽  
Problem Statement ◽  
Fundamental Forces

This paper presents a mathematical model that provides analytic connection between four fundamental forces (interactions), by using modified reciprocal theorem,derived in the paper, as a convenient template. The essential premise of this work is to demonstrate that if we obtain with a form of the Yukawa potential function [as a meromorphic univalent function], we may eventually obtain the Coloumb Potential as a univalent function outside of the unit disk. Finally, we introduce the new problem statement about assigning Meijer's G-functions to Yukawa and Coloumb potentials as an open problem.

scholarly journals Compact Differences of Composition Operators on Bergman Spaces Induced by Doubling Weights

2021 ◽  
Author(s):  
Bin Liu ◽  
Jouni Rättyä ◽  
Fanglei Wu
Keyword(s):  
Bergman Space ◽  
Open Problem ◽  
Lebesgue Space ◽  
Composition Operators ◽  
Bergman Spaces ◽  
Weighted Bergman Space ◽  
Carleson Measures ◽  
Doubling Weights ◽  
The Way

AbstractBounded and compact differences of two composition operators acting from the weighted Bergman space $$A^p_\omega $$ A ω p to the Lebesgue space $$L^q_\nu $$ L ν q , where $$0<q<p<\infty $$ 0 < q < p < ∞ and $$\omega $$ ω belongs to the class "Equation missing" of radial weights satisfying two-sided doubling conditions, are characterized. On the way to the proofs a new description of q-Carleson measures for $$A^p_\omega $$ A ω p , with $$p>q$$ p > q and "Equation missing", involving pseudohyperbolic discs is established. This last-mentioned result generalizes the well-known characterization of q-Carleson measures for the classical weighted Bergman space $$A^p_\alpha $$ A α p with $$-1<\alpha <\infty $$ - 1 < α < ∞ to the setting of doubling weights. The case "Equation missing" is also briefly discussed and an open problem concerning this case is posed.

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