Foundations of Physics

, Volume 30, Issue 10, pp 1765–1799 | Cite as

Pre-BZ and Degenerate BZ Posets: Applications to Fuzzy Sets and Unsharp Quantum Theories

  • G. Cattaneo
  • R. Giuntini
  • S. Pulmannovà


Two different generalizations of Brouwer–Zadeh posets (BZ posets) are introduced. The former (called pre-BZ poset) arises from topological spaces, whose standard power set orthocomplemented complete atomic lattice can be enriched by another complementation associating with any subset the set theoretical complement of its topological closure. This complementation satisfies only some properties of the algebraic version of an intuitionistic negation, and can be considered as, a generalized form of a Brouwer negation. The latter (called degenerate BZ poset) arises from the so-called special effects on a Hilbert space. It is shown that the standard Brouwer negation for effect operators produces a degenerate BZ poset with respect to the order induced from the partial sum operation.


Hilbert Space Quantum Theory Special Effect Topological Space Effect Operator 
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Copyright information

© Plenum Publishing Corporation 2000

Authors and Affiliations

  • G. Cattaneo
    • 1
  • R. Giuntini
    • 2
  • S. Pulmannovà
    • 3
  1. 1.Dipartimento di Informatica, Sistemistica e ComunicazioneUniversità di Milano-BicoccaMilanoItaly;
  2. 2.Dipartimento di Scienze Pedagogiche e FilosoficheUniversità di CagliariCagliariItaly;
  3. 3.Mathematical InstituteSlovak Academy of SciencesBratislavaSlovakia;

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