Conditional Objects, Possibility Theory and Default Rules
Didier Dubois, Henri M. Prade · 1995
Abstract Conditioning is very often considered in connection with probability; both look strongly entwined in the usual notion of conditional probability. This connection has created a gap between probability theory and logic: while the former seems to ignore material implication when representing conditional knowledge, the latter has no genuine tool to account for conditioning. This chapter is an investigation of the relationship between conditional objects of the form q\p, obtained as a qualitative counterpart to conditional probabilities P(g|p), and non-monotonic reasoning. Viewed as an inference rule, the conditional object possesses properties of a well-behaved non-monotonic consequence relation. The basic tool is the 3-valued semantics of conditional objects that differs from the preferential semantics of Lehmann and colleagues and does not require probabilistic semantics. Semantic entailment of a conditional object q\p from a knowledge base made of conditional objects is equivalent to the inference of the conditional assertion p |˜ q in Lehmann’s system P.