On varieties of MV-algebras with internal states

• Published in: International journal of approximate reasoning Vol. 51; no. 6; pp. 680 - 694
• Main Authors: Di Nola, A., Dvurečenskij, A., Lettieri, A.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier Inc 01.07.2010; Elsevier
• Subjects: Applied sciences; Approximation; Computer science; control theory; systems; Exact sciences and technology; Internal state; Logical, boolean and switching functions; Operators; Reasoning; State MV-algebra; State-morphism MV-algebra; State-morphism-operator; Subdirectly irreducible state MV-algebra; Theoretical computing; State MV-algebra; Subdirectly irreducible state MV-algebra; State-morphism-operator; State-morphism MV-algebra; Internal state; Irreducible operator; Operator algebra; Multivalued logic; Morphism

In [4,5] the authors introduced the variety SMV of MV-algebras with an internal operator, state MV-algebras. In [2,3] the authors gave a stronger version of state MV-algebras, called state-morphism MV-algebras. In this paper we continue the studies presented in [2,3] just looking at several proper s...