 In (Hyttinen, Paolini, &amp; Väänänen 2015) a variant of propositional team logic, called quantum team logic, is introduced. In this formalism, teams are replaced by quantum teams, which differ from the ordinary teams of propositional team logic in that they allow for the values of certain variables to be indeterminate with respect to certain valuations and in that they allow for multiple instances of the same valuation (thus adding a quantitative aspect to team semantics). A semantics is then defined over quantum teams for a language that allows for the specification of inequalities concerning the probabilities of events, and a sound and complete proof system is developed for it; and finally, it is shown that Bell’s inequalities admit counterexamples in this systems, as they do according to the predictions of quantum mechanics and according to experimental evidence (Einstein, Podolsky, &amp; Rosen 1935; Bell 1964; Aspect, Grangier, &amp; Roger 1981), while they do not so in the classical version of this framework.