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 conditional 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 definition of the set of all
conditional assertions entailed by a conditional knowledge base. In a previous
paper, S. Kraus and the authors defined 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 nonmonotonic inference procedure should define 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
defined and shown to provide an attractive answer to the question of the title.
Global properties of this closure operation are proved: it is a cumulative
operation. It is also computationally tractable. This paper assumes the
underlying language is propositional.
