The relationship between KLM and MAK models for nonmonotonic inference operations

Abstract

The purpose of this note is to make quite clear the relationship between two variants of the general notion of a preferential model for nonmonotonic inference: the models of Kraus, Lehmann and Magidor (KLM models) and those of Makinson (MAK models).

On the one hand, we introduce the notion of the core of a KLM model, which suffices to fully determine the associated nonmonotonic inference relation. On the other hand, we slightly amplify MAK models with a monotonic consequence operation as additional ingredient.

We give two equivalent characterizations of the cores of KLM models: they are precisely the amplified MAK models whose satisfaction relation:

• may be expressed as the intersection of some non-empty family of satisfaction relations each of which is classically well-behaved; or

• satisfies certain syntactic conditions.

This gives corollary characterizations of certain particular classes of KLM models, notably those that are (in their terminology) cumulative and more specifically those they call preferential.