A unified framework for the algebra of unsharp quantum mechanics

Gianpiero Cattaneo, Stanley Gudder

Gianpiero Cattaneo, Federico Laudisa

David J. Foulis, M. K. Bennett

Gianpiero Cattaneo

Stanley Gudder

Various versions of noncommutative probability theory are surveyed. It is stressed that the main motivation and applications of these noncommutative theories is quantum mechanics. A review of traditional probability theory and its unsharp version are presented. Sharp and unsharp Hilbert space probability theories are considered next. We then present a general discussion of observables and statistical maps. Finally, we consider sequential effect algebras and show that they unify and generalize all of these types of probability theories.

Gianpiero Cattaneo, María Luisa Dalla Chiara, Roberto Giuntini

A basic aim of the unsharp approaches to quantum mechanics is to provide a mathematization of some ambigous aspects, that seem to be characteristic of the “concrete reality”. This has suggesten different forms of paraconsistent quantum logic. We work in the framework of a general semantics for physical theories, which concerns both the classical and quantum case.