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.

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.

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].

scholarly journals Generalized continuous and left-continuous t-norms arising from algebraic semantics for fuzzy logics

2010 ◽  
Vol 180 (8) ◽  
pp. 1354-1372 ◽  
Author(s):  
Carles Noguera ◽  
Francesc Esteva ◽  
Lluís Godo
Keyword(s):  
Algebraic Semantics ◽  
Fuzzy Logics

An Algebraic Aspect of Correspondences Between Implicational Fragment Logics and Fuzzy Logics

2015 ◽  
Vol 19 (6) ◽  
pp. 861-866
Author(s):  
Mayuka F. Kawaguchi ◽  
◽  
Michiro Kondo ◽  
Keyword(s):  
Partially Ordered Set ◽  
Ordered Set ◽  
Unit Interval ◽  
Axiomatic System ◽  
Research Report ◽  
Algebraic Semantics ◽  
Fuzzy Logics ◽  
The Real ◽  
Partially Ordered ◽  
Algebraic Aspect

This research report treats a correspondence between implicational fragment logics and fuzzy logics from the viewpoint of their algebraic semantics. The authors introduce monotone BI-algebras by loosening the axiomatic system of BCK-algebras. We also extend the algebras of fuzzy logics with weakly-associative conjunction from the case of the real unit interval to the case of a partially ordered set. As the main result of this report, it is proved that the class of monotone BI-algebras with condition (S) coincides with the class of weakly-associative conjunctive algebras.

A Mathematical Setting for Fuzzy Logics

1997 ◽  
Vol 05 (03) ◽  
pp. 223-238 ◽  
Author(s):  
Mai Gehrke ◽  
Carol Walker ◽  
Elbert Walker
Keyword(s):  
Fuzzy Logic ◽  
Propositional Logic ◽  
Normal Forms ◽  
Unit Interval ◽  
Fuzzy Logics ◽  
Real Numbers ◽  
Truth Values ◽  
Finite Algebras ◽  
Finite Algorithms ◽  
Interval Valued

The setup of a mathematical propositional logic is given in algebraic terms, describing exactly when two choices of truth value algebras give the same logic. The propositional logic obtained when the algebra of truth values is the real numbers in the unit interval equipped with minimum, maximum and -x=1-x for conjunction, disjunction and negation, respectively, is the standard propositional fuzzy logic. This is shown to be the same as three-valued logic. The propositional logic obtained when the algebra of truth values is the set {(a, b)|a≤ b and a,b∈[0,1]} of subintervals of the unit interval with component-wise operations, is propositional interval-valued fuzzy logic. This is shown to be the same as the logic given by a certain four element lattice of truth values. Since both of these logics are equivalent to ones given by finite algebras, it follows that there are finite algorithms for determining when two statements are logically equivalent within either of these logics. On this topic, normal forms are discussed for both of these logics.

scholarly journals Distinguished algebraic semantics for t-norm based fuzzy logics: Methods and algebraic equivalencies

2009 ◽  
Vol 160 (1) ◽  
pp. 53-81 ◽  
Author(s):  
Petr Cintula ◽  
Francesc Esteva ◽  
Joan Gispert ◽  
Lluís Godo ◽  
Franco Montagna ◽  
...  
Keyword(s):  
Algebraic Semantics ◽  
Fuzzy Logics

scholarly journals Monadic BL-algebras: The equivalent algebraic semantics of Hájek's monadic fuzzy logic

2017 ◽  
Vol 320 ◽  
pp. 40-59 ◽  
Author(s):  
Diego Castaño ◽  
Cecilia Cimadamore ◽  
José Patricio Díaz Varela ◽  
Laura Rueda
Keyword(s):  
Fuzzy Logic ◽  
Algebraic Semantics

scholarly journals Definition of manufacturability - product of mathematical expressions and fuzzy logic for his early design

2013 ◽  
Vol 2 (3) ◽  
pp. 239
Author(s):  
Radivoje Borivoje Antic ◽  
Slavica Cvetkovic ◽  
Branko Pejovic ◽  
Milan Cvetkovic
Keyword(s):  
Fuzzy Logic ◽  
Robust Design ◽  
New Product ◽  
Fuzzy Logics ◽  
Early Design ◽  
Mathematical Expressions ◽  
Definition Of

The paper explaines manufacturability of products for robust design of a new product. Explained mathematical expressions of fuzzy logics describe manufacturability. Provides an example of using the model for the determination of the tmanufacturability.

scholarly journals Expert Evaluation of Ecological and Economic Risks of Implementing Engineering Innovations by Coal-Mining Enterprises Based on Fuzzy Logic

2019 ◽  
Vol 297 ◽  
pp. 07005
Author(s):  
Elena Raevskaya ◽  
Alexander Pimonov ◽  
Vladimir Mihailov
Keyword(s):  
Decision Making ◽  
Fuzzy Logic ◽  
Decision Support ◽  
Coal Mining ◽  
Mining Industry ◽  
Risk Indicators ◽  
Qualitative Assessment ◽  
Expert Evaluation ◽  
Fuzzy Logics ◽  
Complex Approach

The article is about a complex approach based on the method of analyzing hierarchies and using of fuzzy logics for assessment of risks deals with engineering innovations in coal-mining industry. This approach allows evaluating both quantitative and qualitative risk indicators of compared alternative innovative mechanisms and equipment, does not depend on a field of expertise, thus it makes possible to attract specialists with competencies in various fields of knowledge. Such kind of approach allows making a qualitative assessment of the situation on the basis of formalized logical conclusions, making decision making comfortable and accessible to any specialist. The proposed methodology is implemented as a part of a decision support system.

scholarly journals Q-Filters of Quantum B-Algebras and Basic Implication Algebras

Symmetry ◽  
2018 ◽  
Vol 10 (11) ◽  
pp. 573 ◽  
Author(s):  
Xiaohong Zhang ◽  
Rajab Borzooei ◽  
Young Jun
Keyword(s):  
Algebraic Semantics ◽  
Fuzzy Logics ◽  
Quantum Logics ◽  
Filter Theory ◽  
Implication Algebras ◽  
Implication Algebra

The concept of quantum B-algebra was introduced by Rump and Yang, that is, unified algebraic semantics for various noncommutative fuzzy logics, quantum logics, and implication logics. In this paper, a new notion of q-filter in quantum B-algebra is proposed, and quotient structures are constructed by q-filters (in contrast, although the notion of filter in quantum B-algebra has been defined before this paper, but corresponding quotient structures cannot be constructed according to the usual methods). Moreover, a new, more general, implication algebra is proposed, which is called basic implication algebra and can be regarded as a unified frame of general fuzzy logics, including nonassociative fuzzy logics (in contrast, quantum B-algebra is not applied to nonassociative fuzzy logics). The filter theory of basic implication algebras is also established.

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