What Does a Conditional Knowledge Base Entail?

This paper presents a logical approach to nonmonotonic reasoning based on the notion of a nonmonotonic consequence relation A condi tional knowledge base consisting of a set of conditional assertions of the type if then represents the explicit defeasible knowledge an agent has about the way the world generally behaves We look for a plausible de nition of the set of all conditional assertions entailed by a conditional knowledge base In a previous paper S Kraus and the authors de ned and studied preferential consequence relations They noticed that not all preferential relations could be considered as reasonable inference procedures This paper studies a more restricted class of consequence relations rational relations It is argued that any reasonable nonmono tonic inference procedure should de ne a rational relation It is shown that the rational relations are exactly those that may be represented by a ranked preferential model or by a non standard probabilistic model The rational closure of a conditional knowledge base is de ned and shown to provide an attractive answer to the question of the title Global prop erties of this closure operation are proved it is a cumulative operation It is also computationally tractable This paper assumes the underlying language is propositional