A Bell Inequality Analog in Quantum Measure Theory

One obtains Bell's inequalities if one posits a hypothetical joint probability distribution, or measure, whose marginals yield the probabilities produced by the spin measurements in question. The existence of a joint measure is in turn equivalent to a certain local causality condition known as ``screening off''. We show that if one assumes, more generally, a joint ``quantal measure'', or ``decoherence functional'', one obtains instead an analogous inequality weaker by a factor of sqrt(2). The proof of this ``Tsirel'son inequality'' is geometrical and rests on the possibility of associating a Hilbert space to any strongly positive quantal measure. These results lead both to a question: ``Does a joint measure follow from some quantal analog of `screening off'?'', and to the observation that non-contextual hidden variables are viable in histories-based quantum mechanics, even if they are excluded classically