Modelling of Non-Commuting Measurements

In the paper we propose an approach which allows to discuss on formal level non-commuting measurements. Such measurements 'disturb' a measured system and change its states. The key structure used in the description of such measurements is the structure of ortho-poset (which is a Boolean lattice in the classical case of commuting measurements). States of the system are realized as probabilistic measures on the ortho-poset. We give an application of the proposed approach to decision-making under 'non-classical' indeterminacy and to modelling 'non-classical' preferences.