Abstract
In the paper, the EPR paradox is explored by the approach of quantum supervaluationism that leads to a "gappy" semantics with the propositions giving rise to truth-value gaps. Within this approach, the statement, which asserts that in the singlet state the system of two (i.e., A and B) spin-1/2 particles possesses the a priori property "spin A is up and spin B is down along the same axis" or "spin A is down and spin B is up along the same axis", does not have the truth-value at all. Consequently, after the verification of, say, the proposition "spin A is up along the z-axis", the statistical population describing the valuation of the logical connective "spin B is down along the z-axis and spin B is up (down) along the x-axis" would have no elements.