, H .Bezzazi ^{1,2}and RP .Perez ^{1,3}D .Makinson ^{4}

and ^{1}LIFL U.A. 369 du CNRS, Cite Scientifique, 59655Villeneue d'Ascq Cedex,France ^{2}Universite de Lille II, Faculte de Droit, 59000Lille ,France . E-mail: bezzazi@lifl.fr^{3}Universite de Lille I, Eudil, 59655Villeneue d'Ascq ,France . E-mail: pino@lifl.fr^{4}Les Etangs B2, La Ronce, 92410Ville d'Avray ,France . E-mail: d.makinson@unesco.org

ABSTRACT Lehmann, Magidor and others hae investigated the effects of adding the non-Horn rule of

rational monotonyto the rules for preferential inference in nonmonotonic reasoning. In particular, they have shown that every inference relation satisfying those rules is generated by some ranked preferential model.We explore the effects of adding a number of other non-Horn rules that are stronger than or incomparable with rational monotony, but which are still weaker than plain monotony. Distinguished among these is a rule of

determinancy preservation, equivalent to one ofrational transitivity, for which we establish a representation theorem in terms ofquasi-linearpreferential models. An important tool in the proof of the representation theorem is the following purely semantic result, implicit in work of Freund, but here established by a more direct argument: every ranked preferential model generates the same inference relation as some ranked preferential model that iscollapsed, in the sense of being both injective and such that each of its states is minimal for some formula.We also consider certain other non-Horn rules which are incomparable with monotony but are implied by conditional excluded middle, and establish a representation result for a central one among them, which we call

fragmented disjunction, equivalent tofragmented conjunction, in terms ofalmost linearpreferential models.Finally, we consider briefly some curious Horn rules beyond the preferential ones but weaker than monotony, notably those which we call

conjunctive insistenceandn-monotony.

Pages:

605 -631

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