  Based on ideas of quantum theory of open systems we propose the consistent
approach to the formulation of logic of plausible propositions. To this end we
associate with every plausible proposition diagonal matrix of its likelihood
and examine it as density matrix of relevant quantum system. We are showing
that all logical connectives between plausible propositions can be represented
as special positive valued transformations of these matrices. We demonstrate
also the above transformations can be realized in relevant composite quantum
systems by quantum engineering methods. The approach proposed allows one not
only to reproduce and generalize results of well-known logical systems
(Boolean, Lukasiewicz and so on) but also to classify and analyze from unified
point of view various actual problems in psychophysics and social sciences.
