Commutative basic algebras and non-associative fuzzy logics

DOI10.1007/s00153-009-0125-7zbMath1168.03014OpenAlexW1988000631MaRDI QIDQ1016506

Radomír Halaš, Michal Botur

Publication date: 6 May 2009

Published in: Archive for Mathematical Logic (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00153-009-0125-7

zbMATH Keywords

MV-algebraŁukasiewicz logicGödel logicnon-associative fuzzy logic

Mathematics Subject Classification ID

Fuzzy logic; logic of vagueness (03B52) Other algebras related to logic (03G25) MV-algebras (06D35)

Related Items (30)

Pseudo Commutative Double Basic Algebras ⋮ Very true on CBA fuzzy logic ⋮ The logic induced by effect algebras ⋮ Double basic algebras ⋮ On varieties of basic algebras ⋮ A representation of skew effect algebras ⋮ Study strong Sheffer stroke non-associative MV-algebras by fuzzy filters ⋮ A non-associative generalization of effect algebras ⋮ A non-associative generalization of Hájek's BL-algebras ⋮ The propositional logic induced by means of basic algebras ⋮ Properties of non-associative MV-algebras ⋮ States on commutative basic algebras ⋮ Tense operators on basic algebras ⋮ Pre-ideals of basic algebras ⋮ Two kinds of parameterized metrics: construction, topological properties and applications ⋮ Interior and closure operators on commutative basic algebras ⋮ Operators on Pavelka's algebras induced by fuzzy relations ⋮ MP-CLOSED SUBSETS IN BASIC ALGEBRAS ⋮ There exist subdirectly irreducible commutative basic algebras of an arbitrary infinite cardinality which are not MV-algebras ⋮ Unnamed Item ⋮ Strong NMV-algebras, commutative basic algebras and naBL-algebras ⋮ The variety of modular basic algebras generated by MV-chains and horizontal sums of three-element chain basic algebras ⋮ Reduced axioms for the propositional logics induced by basic algebras ⋮ Axiomatization of non-associative generalisations of Hájek's BL and psBL ⋮ Residuated structures and orthomodular lattices ⋮ Operations and structures derived from non-associative MV-algebras ⋮ BCC-algebras and residuated partially-ordered groupoid ⋮ Material implications in lattice effect algebras ⋮ Q-filters of quantum B-algebras and basic implication algebras ⋮ On residuation in multilattices: filters, congruences, and homomorphisms.

Cites Work

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• Effect algebras and unsharp quantum logics.
• Towards more realistic (e.g., non-associative) ``and - and ``or-operations in fuzzy logic
• On copulas, quasicopulas and fuzzy logic
• Latent connectives in human decision making
• An introduction to copulas. Properties and applications
• Metamathematics of fuzzy logic
• Generalization of blocks for \(D\)-lattices and lattice-ordered effect algebras
• Algebraic foundations of many-valued reasoning
• A basic algebra is an MV-algebra if and only if it is a BCC-algebra
• Conjunctors and their residual implicators: characterizations and construction methods
• Complete commutative basic algebras
• Modeling holistic fuzzy implication using co-copulas
• Weakly implicative (fuzzy) logics. I: Basic properties
• Independence of axiom system of basic algebras
• MV-algebras: a variety for magnitudes with archimedean units
• An example of a commutative basic algebra which is not an MV-algebra
• Algebraic Analysis of Many Valued Logics
• Algebraizable logics
• Residuated Lattices

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