Possibility theory as a basis for preference propagation in automated reasoning

Possibility theory is proposed as a tool for encoding and propagating preference relations among possible interpretations or worlds, as well as certainty or priority degrees attached to logic sentences. The following points are particularly considered: (i) the representation of certainty- or possibility-qualified statements and its application to a typology of fuzzy rules; (ii) the principle of minimum specificity as the possibilistic counterpart of the maximal entropy principle; (iii) hypergraph methods for implementing the combination/projection paradigm of approximate reasoning; and (iv) the expression of the semantics of a set of certainty-weight logical formulas in possibilistic logic in terms of a possibility distribution on a set of interpretations. Simple examples of uncertain reasoning, analogical reasoning, interpolative reasoning, qualitative or temporal reasoning are provided in this framework