Characterizing General Preferential Entailments

A preferential entailment is defined by a binary relation, or “preference relation”. This relation can be either among interpretations or among sets of interpretations. The relation can be also among “states” which are “copies of interpretations”, or “copies of sets of interpretations”. This provides four kinds of preferential entailments. The paper deals mainly with propositional logic, however this work applies also to the first order case and indications are given in order to describe the situation in first order logic. What we do here is to provide a characterization result for the most general version described above, and to compare with the known characterizations of the “simplest” versions. It appears that the apparently most complicated notion possesses by far the simplest characterization result. A by-product of our results is that the definition can be simplified without loss of generality: we can define directly the relation among sets of interpretations, eliminating the need for “states” in this case. Thus only three kinds of “preferential entailment” remain.