Basic algebras, logics, trends and applications

DOI10.1142/S1793557115500400zbMath1330.06006MaRDI QIDQ5899524

Ivan Chajda

Publication date: 13 November 2015

Published in: Asian-European Journal of Mathematics (Search for Journal in Brave)

zbMATH Keywords

basic algebrascongruencespropositional logicorthomodular latticesMV-algebrasvarietiesfiltersbounded latticescongruence propertiesaxiom systemsantitone involutionsimplication reductsinterval basic algebras

Mathematics Subject Classification ID

Equational logic, Mal'tsev conditions (08B05) Other algebras related to logic (03G25) Complemented lattices, orthocomplemented lattices and posets (06C15) MV-algebras (06D35) Quantum logic (03G12) Other generalizations of distributive lattices (06D75)

Related Items

Pseudo Commutative Double Basic Algebras, The Sheffer stroke operation reducts of basic algebras, States on implication basic algebras, Basic algebras and L-algebras, Interval Sheffer stroke basic algebras and Yang-Baxter equation, Reduced axioms for the propositional logics induced by basic algebras, Material implications in lattice effect algebras, Representations of Sheffer stroke algebras and Visser algebras, A view on state operators in Sheffer stroke basic algebras

Cites Work

• Metamathematics of fuzzy logic
• The writing of the MV-algebras
• Algebraic foundations of many-valued reasoning
• The logic of quantum mechanics
• REGULARITY OF GENERALIZED MV-ALGEBRAS
• Proof of an Axiom of Lukasiewicz
• A New Proof of the Completeness of the Lukasiewicz Axioms
• Commutative directoids with sectionally antitone bijections
• Horizontal sums of basic algebras
• Algebraizable logics
• MODIFICATIONS OF MV-ALGEBRAS CORRESPONDING TO STRONG ORTHOLATTICES
• Semilattices with sectional mappings
• WHEN IS A BCC-ALGEBRA EQUIVALENT TO AN MV-ALGEBRA?
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item