States in Łukasiewicz logic correspond to probabilities of rational polyhedra

Authors:
Tomáš Kroupa
Affiliations:
Institute of Information Theory and Automation of the ASCR, Pod Vodárenskou věží 4, 182 08 Prague, Czech Republic
Venue:
International Journal of Approximate Reasoning
Year:
2012

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Abstract

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.