On varieties of MV-algebras with internal states

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...

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Published inInternational journal of approximate reasoning Vol. 51; no. 6; pp. 680 - 694
Main Authors Di Nola, A., Dvurečenskij, A., Lettieri, A.
Format Journal Article
LanguageEnglish
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
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Abstract 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 subvarieties of SMV , obtained by imposing suitable conditions on the behavior of the internal operator.
AbstractList 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 subvarieties of SMV , obtained by imposing suitable conditions on the behavior of the internal operator.
In the authors introduced the variety SMV of MV-algebras with an internal operator, state MV-algebras. In the authors gave a stronger version of state MV-algebras, called state-morphism MV-algebras. In this paper we continue the studies presented in just looking at several proper subvarieties of SMV , obtained by imposing suitable conditions on the behavior of the internal operator.
Author Di Nola, A.
Dvurečenskij, A.
Lettieri, A.
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Issue 6
Keywords State MV-algebra
Subdirectly irreducible state MV-algebra
State-morphism-operator
State-morphism MV-algebra
Internal state
Irreducible operator
Operator algebra
Multivalued logic
Morphism
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Snippet 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...
In the authors introduced the variety SMV of MV-algebras with an internal operator, state MV-algebras. In the authors gave a stronger version of state...
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SubjectTerms 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
Title On varieties of MV-algebras with internal states
URI https://dx.doi.org/10.1016/j.ijar.2010.01.017
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