Representations of Uncertainty in Artificial Intelligence: Probability and Possibility

Abstract

Due to its major focus on knowledge representation and reasoning, artificial intelligence was bound to deal with various frameworks for the handling of uncertaintyUncertainty: probability theory, but more recent approaches as well: possibility theory, evidence theory, and imprecise probabilities. The aim of this chapter is to provide an introductive survey that lays bare specific features of two basic frameworks for representing uncertainty: probability theory and possibility theory, while highlighting the main issues that the task of representing uncertainty is faced with. This purpose also provides the opportunity to position related topics, such as rough sets and fuzzy sets, respectively motivated by the need to account for the granularity of representations as induced by the choice of a language, and the gradual nature of natural language predicates. Moreover, this overview includes concise presentations of yet other theoretical representation frameworks such as formal concept analysis, conditional events and ranking functions, and also possibilistic logic, in connection with the uncertainty frameworks addressed here. The next chapter in this volume is devoted to more complex frameworks: belief functions and imprecise probabilities.