  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.
