In today’s world, intelligent systems are expected to handle diverse types of events that can be represented as dichotomy, probabilistic, fuzzy, or mixed statements. This paper proposes an analytic framework called “statemental analysis,” which deals with the operations and truth values of finite and infinite sequences of statements of various categories. The framework treats vagueness and randomness in a unified manner using the concepts of statemental algebra and truth calculus. It allows for generalization of many results in probability theory to statements with significant implications. We demonstrate the utility of the proposed framework with an example of reliability analysis of uncertain systems.
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