2009/07/19 by Ciungu, Lavinia Corina, Dvurečenskij, Anatolij, Hyčko, Marek
#03G12 #06D72 #FOS: Mathematics #Logic (math.LO)
paper · doi:10.48550/arxiv.0907.3268
The concept of a state MV-algebra was firstly introduced by Flaminio and Montagna in \citeFlMo0 and \citeFlMo as an MV-algebra with internal state as a unary operation. Di Nola and Dvurečenskij gave a stronger version of a state MV-algebra in \citeDiDV1, \citeDiDV2. In the present paper we introduce the notion of a state BL-algebra, or more precisely, a BL-algebra with internal state. We present different types of state BL-algebras, like strong state BL-algebras and state-morphism BL-algebras, and we study some classes of state BL-algebras. In addition, we give a sample of important examples of state BL-algebras and present some open problems.