State morphism MV-algebras

We present a complete characterization of subdirectly irreducible MV-algebras with internal states (SMV-algebras). This allows us to classify subdirectly irreducible state morphism MV-algebras (SMMV-algebras) and describe single generators of the variety of SMMV-algebras, and show that we have a continuum of varieties of SMMV-algebras

On consistency of the quantum-like representation algorithm

In this paper we continue to study so called ``inverse Born's rule problem'': to construct representation of probabilistic data of any origin by a complex probability amplitude which matches Born's rule. The corresponding algorithm -- quantum-like representation algorithm (QLRA) was recently proposed by A. Khrennikov [1]--[5]. Formally QLRA depends on the order of conditioning. For two observables $a$ and $b,$ $b| a$- and $a | b$ conditional probabilities produce two representations, say in Hilbert spaces $H^{b| a}$ and $H^{a| b}.$ In this paper we prove that under natural assumptions these two representations are unitary equivalent. This result proves consistency QLRA