Propositional systems in local field theories

We investigate prepositional systems for local field theories, which reflect intrinsically the uncertainties of measurements made on the physical system, and satisfy the isotony and local commutativity postulates of Haag and Kastler. The space-time covariance can be implemented in a natural way in these propositional systems. New techniques are introduced to obtain these propositional systems: the lattice-valued logics. The decomposition of the complete orthomodular lattice-valued logics shows that these logics are more general than the usual two-valued ones and that in these logics there is enough structure to characterize the classical and quantum, nonrelativistic and relativistic local field theories in a natural way. The Hubert modules give the natural inner product spaces (modules) for the realization of the lattice-valued logics.The author is also with the Publishing House of the Hungarian Academy of Sciences, H-1363, Budapest, P.O.B. 24.