Penalty logic and its Link with Dempster-Shafer Theory
This work addresses the problem of handling inconsistency in knowledge bases for AI and logic systems, but it appears incremental as it builds on existing penalty logic concepts.
The paper formalizes penalty logic, which assigns costs to violated formulas to select preferred consistent subsets from inconsistent knowledge bases, establishing its properties and linking it to Dempster-Shafer theory, particularly in infinitesimal cases.
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.