Representation of States on MV-algebras by Probabilities on R-generated Boolean Algebras
Brunella Gerla, Tomáš Kroupa · 2009
Abstract — 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, b ∈ M with s(b) ̸ = 0is extended to the classical conditional probability p(a · b|b) on B(M) of the a-proportion of the event b, given the event b. Keywords — MV-algebra, R-generated Boolean algebra, state, probability, conditional probability