  We propose a general scheme for the "logic" of elementary propositions of
physical systems, encompassing both classical and quantum cases, in the
framework given by Non Commutative Geometry. It involves Baire*-algebras, the
non-commutative version of measurable functions, arising as envelope of the
C*-algebras identifying the topology of the (non-commutative) phase space. We
outline some consequences of this proposal in different physical systems. This
approach in particular avoids some problematic features appearing in the
definition of the state of "initial conditions" in the standard W*-algebraic
approach to classical systems.
