Bosbach states represent a way of probabilisticly evaluating the formulas from various (commutative or non-commutative) many-valued logics. They are defined on the algebras corresponding to these logics with values in [0, 1]. Starting from the observation that in the definition of Bosbach states there intervenes the standard MV-algebra structure of [0, 1], in this paper we introduce Bosbach sta...

Any MV-algebra M can be embedded as a lattice in the Boolean algebra B(M) that is R-generated by M . We relate the study of states on an MV-algebra M to the study of finitely additive probabilities on B(M). In particular, we show that each state on M can be uniquely extended to a finitely additive probability on B(M). In case that M is a PMV-algebra, the conditional state s(a|b) defined for a, ...

The classical Poincaré weak recurrence theorem states that for any probability space (Ω,S, P ), any P -measure preserving transformation T , and any A ∈ S, almost all points of A return to A. In the present paper the Poincaré theorem is proved when the σ-algebra S is replaced by any σ-complete MV-algebra. Keywords— Measure preserving transformation, Poincaré recurrence theorem, σ-complete MV-al...