Syntax-based Default Reasoning as Probabilistic Model-based Diagnosis

TL;DR

This paper models default reasoning as a probabilistic diagnosis problem within the ATMS framework, assigning probabilities to sources and deriving belief functions to support non-monotonic reasoning.

Contribution

It introduces a novel probabilistic approach to default reasoning using model-based diagnosis and belief functions within the ATMS framework.

Findings

Probability assignment on sources induces belief functions.

Different non-monotonic consequence relations are studied and compared.

Prioritized knowledge bases are briefly analyzed.

Abstract

We view the syntax-based approaches to default reasoning as a model-based diagnosis problem, where each source giving a piece of information is considered as a component. It is formalized in the ATMS framework (each source corresponds to an assumption). We assume then that all sources are independent and "fail" with a very small probability. This leads to a probability assignment on the set of candidates, or equivalently on the set of consistent environments. This probability assignment induces a Dempster-Shafer belief function which measures the probability that a proposition can be deduced from the evidence. This belief function can be used in several different ways to define a non-monotonic consequence relation. We study and compare these consequence relations. The -case of prioritized knowledge bases is briefly considered.