Three-dimensional distributions on Quantum logics and MV algebras
Martin Kalina · 2004
It means that if we put two conditions on the event A, the resulting conditional probability is independent of the order of conditions. We show that this is not true in quantum logics (OML) and in MV-algebras. The conditional measure (probability) in OML can be defined by using the so-called s-map. Let L be an OML. The map pn : L n → [0, 1] will be called an sn-map if the following conditions hold: (s1) pn(1, ..., 1) = 1; (s2) if there exist i, j, such that ai ⊥ aj, then pn(a1, ..., an) = 0; (s3) if ai ⊥ bi for some i = 1, ..., n, then pn(a1, ..., ai ∨ bi, ..., an) = pn(a1, ..., ai, ..., an) + pn(a1, ..., bi, ..., an).