States in 艁ukasiewicz logic correspond to probabilities of rational polyhedra

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• 作者：Tomá ; š ; Kroupa ^{kroupa@utia.cas.cz}
• 关键词：Lukasiewicz logic ; McNaughton function ; Many-valued probability ; Rational polyhedron
• 刊名：International Journal of Approximate Reasoning
• 出版年：2012
• 期刊代码：76_0888613x
• 类别：et
• 出版时间：June, 2012
• 卷：53
• 期：4
• 页码：435-446
• 文件大小：375 K

摘要

It will be shown that probabilities of infinite-valued events represented by formulas in 艁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 艁ukasiewicz logic.