Observables in the Logico-Algebraic Approach

Alessandra Di Pierro, Herbert Wiklicky

We present a logico-algebraic approach to probabilistic abstract interpretation based on the ortholattice structure of the projective measurement operators in quantum mechanics. On this base, we present a novel interpretation of quantum measurement as a probabilistic abstraction showing that the measurement of a physical observable essentially corresponds to a static analysis of the observed property.

Karl Svozil

The notion of in terms of nonclassical (paradoxical) properties of probability distributions is refined by concentrating on the nonclassical logico-algebraic structures of the observables supporting such probabilities. These structures often, but not always, induce and are reflected by nonclassical properties of the probability distributions. Two types of contextuality are introduced, originating either in nonclassical probabilities on classical logics, or in genuine nonclassical logics of observables which cannot be faithfully (homomorphically) embedded into (extended) Boolean algebras. It is suggested to substitute the term contextual by indeterminate or value indefinite in the spirit of partial functions of theoretical computer sciences.

C. A. Hooker

M. D. Maia