On varieties of MV-algebras with internal states

Authors:
A. Di Nola;A. Dvurečenskij;A. Lettieri
Affiliations:
Dipartimento di Matematica e Informatica, Università di Salerno, Via Ponte don Melillo, I-84084 Fisciano, Salerno, Italy;Mathematical Institute, Slovak Academy of Sciences, Štefánikova 49, SK-814 73 Bratislava, Slovakia;Dipartimento di Costruzioni e Metodi Matematici in Architettura, Università di Napoli Federico II, via Monteoliveto 3, I-80134 Napoli, Italy
Venue:
International Journal of Approximate Reasoning
Year:
2010

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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.