Birkoff-von Neumann's contention that observational propositions in Quantum Mechanics do not obey the Boolean logic, but the modular logic was suggested by the structure of the Hilbert space, and only indirectly related to the nature of observation in physics. Husimi was the first to undertake the task of establishing directly experimental foundation of quantum logic. The present paper has the same aim as Husimi's early paper, but adopts a different approach. A features of the present paper is its methodology of extracting an algebraic structure from a probabilistic structure. A concrete observational interpratation is given for the first time to the conjunction of two incompatible propositions. A side benefit of this work is clarification of the origin of the Booleanity of the ordinary logic, which has to be sought outside the implicational lattice.