States in Lukasiewicz logic correspond to probabilities of rational polyhedra
It will be shown that probabilities of infinite-valued events represented by formulas in Lukasiewicz 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 Lukasiewicz logic. (C) 2011 Elsevier Inc. All rights reserved.
lukasiewicz logic mcnaughton function many-valued probability rational polyhedron