What does a conditional knowledge base entail?

TL;DR

This paper introduces a logical framework for nonmonotonic reasoning using rational consequence relations derived from conditional knowledge bases, providing a computationally feasible and cumulative inference method.

Contribution

It defines the rational closure for conditional knowledge bases and demonstrates its properties and representation via ranked models, advancing nonmonotonic reasoning theory.

Findings

Rational relations are characterized by ranked models.

The rational closure is a cumulative and computationally tractable inference operation.

The approach applies to propositional languages.

Abstract

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.