What does a conditional knowledge base entail?
<|reference_start|>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.<|reference_end|>
@article{lehmann2002what,
    title={What does a conditional knowledge base entail?},
    author={Daniel Lehmann and Menachem Magidor},
    journal={Journal of Artificial Intelligence, Vol. 55 no.1 (May 1992) pp.
  1-60. Erratum in Vol. 68 (1994) p. 411},
    year={2002},
    number={Leibniz Center for Research in Computer Science TR-88-16 and
  TR-90-10},
    archivePrefix={arXiv},
    eprint={cs/0202022},
    primaryClass={cs.AI}
}