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This aspect will be dealt with in Section 4. In the second place, as we have anticipated in the Introduction, the aim pursued implies confronting oneself with the measurement problem. Indeed, a quantum ontology may arise only within a framework, if it exists at all, in which measurements can be 48 SILVIO BERGIA and VINCENZO FANO described as operations recording a preexistent reality, that is something which can be described as preexistent. As is well known, current views of the measurement problem do not conform to this requirement.

In section 2 we shall report on the characterization of Bell-type inequalities; more explicitly on a theorem (Beltrametti and MaA;zynski, 1994) that provides sufficient and necessary conditions for the inequality 0 S LSI to be a condition of classical representability of the probabilities Pij, Pijk, ... n· In section 3 we shall briefly report on an algorithm, developed by one of the present authors (Del Noce, 1994), based on Boole's method and able to deduce complete sets of Bell-type inequalities for any given empirical situations.

1960), "Measurement of quantum mechanical operators," Physical Review, 120 pp. M. (1961), "Optimal measuring apparatus," Physical Review, 123 pp. 666--668. G. BELTRAMETTI and C. J. MAQZYNSKI Institute of Mathematics, Technical University of Warsaw Warsaw, Poland Abstract. The problem of the intrinsic characterization of classical probabilities is considered. A theorem is given which specifies when an inequality of the form o $ L $ 1, where L is a linear combination of the observed probabilities, is a condition for classical represent ability.

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