Uncertainty.

Some universals of grammar with particular reference to the order of meaningful elements. Uncertainty Almost all information is subject to uncertainty. Uncertainty may arise from inaccurate or incomplete information (e.g., how large are the current U.S. petroleum reserves?), from linguistic imprecision (what exactly do we mean by " petroleum reserves " ?), and from disagreement between information sources. We may even be uncertain about our degree of uncertainty. The representation of uncertainty is intrinsic to the representation of information, which is its dual. Many schemes have been developed to formalize the notion of uncertainty and to mechanize reasoning under uncertainty within KNOWLEDGE-BASED SYSTEMS. Probability is, by far, the best-known and most widely used formalism. However, apparent limitations and difficulties in applying probability have spawned the development of a rich variety of alternatives. These include heuristic approximations to probability used in rule-based expert systems, such as certainty factors (Clancy and Shortliffe 1984); fuzzy set theory and FUZZY LOGIC (Zadeh 1984); interval representations, such as upper probabilities and Dempster-Shafer belief functions (Shafer 1976); NONMONOTONIC LOGICS and default reasoning (Ginsberg 1987); and qualitative versions of probability, such as the Spohn calculus and kappa-calculus. There has been controversy about the assumptions, appropriateness, and practicality of these various schemes, particularly about their use in representing and reasoning about uncertainty in databases and knowledge based systems. It is useful to consider a variety of criteria , both theoretical and pragmatic, in comparing these schemes. The first criterion concerns epistemology: What kinds of uncertainty does each scheme represent? Like most quantitative representations of uncertainty, probability expresses degree of belief that a proposition is true, or that an event will happen, by a cardinal number, between 0 and 1. Fuzzy set theory and fuzzy logic also represent degrees of belief or truth by a number between 0 and 1. Upper probabilities and Dempster-Shafer belief functions represent degrees of belief by a range of numbers between 0 and 1, allowing the expression of ambiguity or ignorance as the extent of the range. Qualitative representations of belief, such as nonmonotonic logic (Ginsberg 1987) and the kappa calculus, often represent degrees of belief on an ordinal scale. In the frequentist view, the probability of an event is the frequency of the event occurring in a large number of similar trials. For example, the probability of heads for a bent coin is the frequency of heads from a large number of tosses …