Yves Moinard and Raymond RollandCircumscriptions from what they cannot do (preliminary report). 
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N:o  Question  Answer(s)  Continued discussion 

1 
8.1 Pat Hayes 
27.1 Yves Moinard 

2 
8.1 Tom Costello 
27.1 Yves Moinard 
What properties must have your preference relation, must it be transitive?
A1. Yves Moinard (27.1):
At this point (the question arrived at the begining of the exposition, corresponding to our prop. 4.2) we require no property at all: < may be just any binary relation. People have already argued about the importance of requiring, or not requiring, transitivity from a knowledge representation perspective, and I have nothing significant to add to these discussions.
Whatever opinion you have on the subject, it is important to give the properties shared by any preferential entailment, without condition for the relation < . Indeed, if in some particular application, it happens that < is transitive, and this fact is never used, then this shows that an important point has been missed somewhere: the study of the ``reasoning properties'' of the preferential entailment used here must be pursued.
Moreover, in our work, it happens later that we need transitivity. Indeed, we establish an exact correspondance between the relation < over the set of models and the converse of the entailment relation between some subset of the set of the inaccessible formulas. As the entailment relation is transitive, we clearly need a transitive relation < . This corresponds roughly to the fact that we need cumulativity if we want to be able to express a preferential entailment from its inaccessible formulas.
Are there any connections between your work and SCAN?
A2. Yves Moinard (27.1):
I do not think there are, but I do not know really. It seems to me unlikely that the formulas encountered while using SCAN have anything to do with the formulas in the set X_{ < } On the other hand, our work is clearly related to some aspects in Bossu and Siegel's method (AI journal, 1985) or Suchenek's method (Journal of Automated Reasoning, 1997).
Till now, we have only investigated the knowledge representation (or common sense reasoning, as we understand the expression) aspects. We would like to investigate in the future the possible interest of our work from a computational point of view.
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