An indispensable function of intelligent systems is to perform logical reasoning in the presence of uncertainty. In this paper, we establish a mathematical framework, called statemental credibility logic (SCL), for inference under uncertainty. The proposed SCL consists of statemental algebra and truth calculus. The statemental algebra deals with the operations of statements which can be representations of deterministic, vague, random events, and their mixture. The truth calculus discusses the evaluation and inference of the truth values of dichotomy, fuzzy, probabilistic statements, and their combinations. We generalize the classical Bayesian networks and develop robust inference methods which have potential to construct more capable and reliable inference engines of intelligent systems.
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