A Comparative Study of Ranking Formulas Based on Consistency

Ranking is ubiquitous in everyday life. This paper is concerned with the problem of ranking information of a knowledge base when this latter is possibly inconsistent. In particular, the key issue is to elicit a plausibility order on the formulas in an inconsistent knowledge base. We show how such ordering can be obtained by using only the inherent structure of the knowledge base. We start by introducing a principled way a reasonable ranking framework for formulas should satisfy. Then, a variety of ordering criteria have been explored to define plausibility order over formulas based on consistency. Finally, we study the behaviour of the different formula ranking semantics in terms of the proposed logical postulates as well as their (in)-compatibility