Perspectives

Abstract

Isomorphic representation of Birkhoff–von Neumann quantum logics, and therefore also of orthomodular lattices L(H) of (orthogonal projections onto) closed subspaces of Hilbert spaces by families of fuzzy sets endowed with Łukasiewicz operations opens new opportunities for solving at least two long-standing problems, namely the development of quantum probability calculus in a way completely analogous to the orthodox Kolmogorovian probability theory, and the construction of a phase space representation of quantum mechanics not plagued by the appearance of negative probabilities.