@article {IOPORT.06080889,
    author       = {Kroupa, Tom\'a\v{s}},
    title        = {States in {\L}ukasiewicz logic correspond to probabilities of rational polyhedra.},
    year         = {2012},
    journal      = {International Journal of Approximate Reasoning},
    volume       = {53},
    number       = {4},
    issn         = {0888-613X},
    pages        = {435-446},
    publisher    = {Elsevier Science Inc. (North-Holland), New York, NY},
    doi          = {10.1016/j.ijar.2011.10.007},
    abstract     = {Summary: It will be shown that probabilities of infinite-valued events represented by formulas in {\L}ukasiewicz propositional logic are in one-to-one correspondence with tight probability measures over rational polyhedra in the unit hypercube. This result generalizes a recent work on rational measures of polyhedra and provides an elementary geometric approach to reasoning under uncertainty with states in {\L}ukasiewicz logic.},
    identifier   = {06080889},
}