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 op erators 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) t he role played by orthomodular posets with respect to orthogonal proje ctions (corresponding to ''sharp'' effects) are analyzed. These struct ures are generally characterized by the splitting of standard orthocom plementation 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) ar e introduced and their relevance with respect to the logic of unsharp quantum mechanics are discussed.