Abstract:
Penalty Logic is a natural and commonsense Knowledge Representation technique to deal with potentially inconsistent beliefs. Penalty Logic allows some kind of compensation between different pieces of information. But one of the main and less studied flaws of Penalty Logic is the influence of the choice of weights on inference: the same pieces of information can provide extremely different results just by changing some weights. This paper concentrates on weightings and on the problem of collisions between interpretations which yield weak conclusions. It focuses more particularly on a family of weightings, the sigma-weightings. We show that some of these weightings avoid collisions but that in the meanwhile they disable the mechanism of compensation (and so the interest) of Penalty Logic. We establish then that two of them are suitable for avoiding collisions and maintaining compensation. We obtain their logical characterizations while considering the weightings only and not the associated formulas. Finally, we propose an original weighting, the Paralex Weighting, that improves even more the previous weightings.