@Article{Navara:INS09,
  IS = { zkontrolovano 21 Jan 2010 },
  UPDATE  = { 2009-12-29 },
  author =     {Navara, Mirko},
  title =      {Existence of states on quantum structures},
  year =       {2009},
  month =      {February},
  pages =      {508--514},
  journal =    {Information Sciences},
  publisher =  {Elsevier},
  address =    {Amsterdam, Netherlands},
  issn =       {0020-0255},
  volume =     {179},
  number =     {5},
  annote = {Orthomodular lattices occurred as generalized event
    structures in the models of probability for quantum mechanics.
    Here we contribute to the question of existence of states
    (=probability measures) on orthomodular lattices.  We prove that
    known techniques do not allow to find examples with less than
    19~blocks (=maximal Boolean subalgebras).  This bound is achieved
    by the example by R.~Mayet.  Although we do not finally exclude
    the existence of other techniques breaking this bound, existence
    of smaller examples is highly unexpected.},
  keywords =   {orthomodular lattice, quantum logic, state, 
                probability measure, block, Boolean subalgebra, 
                pasting},
  project =    {GACR 201/07/1051},
  psurl =      {DOI 10.1016/j.ins.2008.06.011},
}