Penalty Logic and its Link with Dempster-Shafer Theory

Penalty logic, introduced by Pinkas [17], as­ sociates to each formula of a knowledge base the price to pay if this formula is violated. Penalties may be used as a criterion for se­ lecting preferred consistent subsets in an in­ consistent knowledge base, thus inducing a non-monotonic inference relation. A pre­ cise 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 at·e related, es­ pecially in the infinitesimal case.