Penalty logic and its Link with Dempster-Shafer Theory

TL;DR

This paper explores penalty logic, a framework for handling inconsistent knowledge bases through penalties, and establishes its formal properties and connection to Dempster-Shafer theory, especially in the infinitesimal case.

Contribution

It provides a formalization of penalty logic, analyzes its properties, and reveals its relationship with Dempster-Shafer theory, enriching the understanding of non-monotonic reasoning.

Findings

Formal properties of penalty logic established

Connection between penalty logic and Dempster-Shafer theory demonstrated

Insights into non-monotonic inference in inconsistent knowledge bases

Abstract

Penalty logic, introduced by Pinkas, associates to each formula of a knowledge base the price to pay if this formula is violated. Penalties may be used as a criterion for selecting preferred consistent subsets in an inconsistent knowledge base, thus inducing a non-monotonic inference relation. A precise formalization and the main properties of penalty logic and of its associated non-monotonic inference relation are given in the first part. We also show that penalty logic and Dempster-Shafer theory are related, especially in the infinitesimal case.