What does a conditional knowledge base entail?

What does a conditional knowledge base entail?

18 Feb 2002 | Daniel Lehmann, Menachem Magidor
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. The paper studies a more restricted class of consequence relations, called rational relations, which are exactly those that may be represented by a ranked preferential model or a 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. It is shown that the rational closure is a cumulative operation and computationally tractable. The paper also discusses the computational complexity of preferential entailment, showing that it is co-NP-complete. The paper introduces the concept of rationality, which is central to the study of nonmonotonic reasoning. It argues that any reasonable nonmonotonic inference procedure should define a rational relation. The paper also presents a representation theorem for rational relations, showing that they can be characterized in terms of ranked models. The paper concludes that preferential entailment is not a satisfactory answer to the question of the title, as it does not provide a rational relation. Instead, the paper proposes the concept of rational closure as a more suitable answer.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. The paper studies a more restricted class of consequence relations, called rational relations, which are exactly those that may be represented by a ranked preferential model or a 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. It is shown that the rational closure is a cumulative operation and computationally tractable. The paper also discusses the computational complexity of preferential entailment, showing that it is co-NP-complete. The paper introduces the concept of rationality, which is central to the study of nonmonotonic reasoning. It argues that any reasonable nonmonotonic inference procedure should define a rational relation. The paper also presents a representation theorem for rational relations, showing that they can be characterized in terms of ranked models. The paper concludes that preferential entailment is not a satisfactory answer to the question of the title, as it does not provide a rational relation. Instead, the paper proposes the concept of rational closure as a more suitable answer.
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