FUZZY QUANTUM LOGIC .2. THE LOGICS OF UNSHARP QUANTUM-MECHANICS

A survey of the main results of the Italian group about the logics of unsharp quantum mechanics is presented. In particular partial ordered structures playing with respect to effect operators (linear bounded operators F on a Hilbert space H such that for-allpsi is-an-element-of H, 0 less-than-or-equal-to [psi\Fpsi] less-than-or-equal-to \\psi\\2) the role played by orthomodular posets with respect to orthogonal projections (corresponding to ''sharp'' effects) are analyzed. These structures are generally characterized by the splitting of standard orthocomplementation on projectors into two nonusual orthocomplementations (a fuzzy-like and an intuitionistic-like) giving rise to different kinds of Brouwer-Zadeh (BZ) posets: de Morgan BZ posets, BZ* posets, and BZ3 posets. Physically relevant generalizations of ortho-pair semantics (paraconsistent, regular paraconsistent, and minimal quantum logics) are introduced and their relevance with respect to the logic of unsharp quantum mechanics are discussed.