What does a conditional knowledge base entail?

*(English)*Zbl 0762.68057
Artif. Intell. 55, No. 1, 1-60 (1992); erratum ibid. 68, No. 2, 411 (1994).

Summary: The 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.

S. Kraus, D. Lehmann and M. Magidor [“Nonmonotonic reasoning, preferential models and cumulative logics”, Artif. Intell. 44, No. 1/2, 167–207 (1990; Zbl 0782.03012)] defined and studied preferential consequence relations. They noticed that not all preferential relations could be considered as reasonable inference procedures.

The 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 (nonstandard) probabilistic model. The rational closure of a conditional knowledge base is defined and shown to prove 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.

S. Kraus, D. Lehmann and M. Magidor [“Nonmonotonic reasoning, preferential models and cumulative logics”, Artif. Intell. 44, No. 1/2, 167–207 (1990; Zbl 0782.03012)] defined and studied preferential consequence relations. They noticed that not all preferential relations could be considered as reasonable inference procedures.

The 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 (nonstandard) probabilistic model. The rational closure of a conditional knowledge base is defined and shown to prove 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.

##### MSC:

68T30 | Knowledge representation |

68T15 | Theorem proving (deduction, resolution, etc.) (MSC2010) |

68T27 | Logic in artificial intelligence |

##### Keywords:

nonmonotonic reasoning; nonmonotonic consequence relation; conditional knowledge base; preferential consequence relations; rational closure
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\textit{D. Lehmann} and \textit{M. Magidor}, Artif. Intell. 55, No. 1, 1--60 (1992; Zbl 0762.68057)

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