Some generalizations of fuzzy structures in quantum computational logic

Quantum computational logics provide a fertile common ground for a uni ed treatment of vagueness and uncertainty. In this paper we describe an approach to the logic of quantum computation that has been recently taken up and developed by the present authors. Special attention will be devoted to a generalisation of Chang's MV algebras (called quasi-MV algebra) which abstracts over the algebra whose universe is the set of qumixes of the 2-dimensional complex Hilbert space, as well as to its expansions by additional quantum connectives. We furthermore explore some future research perspectives, also in the light of some recent limitative results whose general signi cance will be duly assessed.