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Models for many-valued probabilistic reasoning. (English) Zbl 1237.06005
The authors introduced MV-algebras with an internal state, called SMV-algebras, to incorporate the notion of MV-algebraic “state” introduced by the present reviewer in his paper [Stud. Log. 55, No. 1, 113–127 (1995; Zbl 0836.03016)]. While the states of an MV-algebra $$A$$ are just the restrictions to $$A$$ of positive normalized linear functionals defined on the unital lattice-ordered abelian group of $$A$$, in SMV-algebras states are internal operations. In this paper SMV-semantics is linked to Kripke semantics via sigma-simple SMV-algebras. The final part of this paper is devoted to the complexity of the tautology problem for the resulting logics.

##### MSC:
 06D35 MV-algebras 03B50 Many-valued logic 03G12 Quantum logic
##### Keywords:
SMV-algebra; MV-algebra; state; probabilistic Kripke models; PSPACE
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