Conditional probability on MV-algebras

An appropriate definition of a conditional probability on an MV-algebra was an open problem mentioned in Riečan and Mundici (Handbook of Measure Theory, North-Holland, Amsterdam, 2002). We propose some concept of conditional probability (state) on a σ-complete MV-algebra with product. Its basic properties will be proven and it will also be demonstrated that the conditional probability in classical probability theory is a special case of this definition. Moreover, the paper contains also a discussion of the interpretation of fuzzy sets and conditioning in fuzzy probability theory.