Probability Measures and Projections on Quantum Logics

The present paper is devoted to modelling of a probability measure of logical connectives on a quantum logic (QL), via a G-map, which is a special map on it. We follow the work in which the probability of logical conjunction, disjunction and symmetric difference and their negations for non-compatible propositions are studied. We study such a G-map on quantum logics, which is a probability measure of a projection and show, that unlike classical (Boolean) logic, probability measure of projections on a quantum logic are not necessarilly pure projections. We compare properties of a G-map on QLs with properties of a probability measure related to logical connectives on a Boolean algebra.