Part I. Invited Papers Dedicated to Constantin Piron

Foundations of Physics

, Volume 24, Issue 8, pp 1161-1177

First online:

Partial and unsharp quantum logics

  • M. L. Dalla ChiaraAffiliated withDipartimento di Filosofia, Università di Firenze
  • , R. GiuntiniAffiliated withDipartimento di Filosofia, Università di Firenze

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Abstract

The total and the sharp character of orthodox quantum logic has been put in question in different contexts. This paper presents the basic ideas for a unified approach to partial and unsharp forms of quantum logic. We prove a completeness theorem for some partial logics based on orthoalgebras and orthomodular posets. We introduce the notion of unsharp orthoalgebra and of generalized MV algebra. The class of all effects of any Hilbert space gives rise to particular examples of these structures. Finally, we investigate the relationship between unsharp orthoalgebras, generalized MV algebras, and orthomodular lattices.