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2010 | OriginalPaper | Buchkapitel
Uncertain Logic
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Uncertain logic is a generalization of mathematical logic for dealing with uncertain knowledge via uncertainty theory. The first model is uncertain propositional logic designed by Li and Liu [96] in which the truth value of an uncertain proposition is defined as the uncertain measure that the proposition is true. An important contribution is the truth value theorem by Chen and Ralescu [18] that provides a numerical method for calculating the truth value of uncertain formulas. The second model is uncertain predicate logic proposed by Zhang and Peng [227] in which an uncertain predicate proposition is defined as a sequence of uncertain propositions indexed by one or more parameters.
One advantage of uncertain logic is the well consistency with classical logic. For example, uncertain logic obeys the law of truth conservation and is consistent with the law of excluded middle and the law of contradiction. This chapter will introduce uncertain propositional logic and uncertain predicate logic.