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...ot of concern. One possible way to deal with this difficulty is to make certain assumptions about the preference ordering. In particular, it is possible to adopt the default reasoning scheme System Z =-=[23]-=- in this context. Given a set of conditional constraints, System Z enforces the assumption that worlds are assumed to be as preferred as possible consistent with these constraints. In other words, wor...

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...89; Grosof 1991),sapproaches which handle implicit priority infor-smation based on the specificity of defaults (Tou-sretzky 1986; Touretzky, Horty, & Thomason 1987;sTouretzky, Thomason, & Horty 1991; =-=Pearl 1990-=-;sGeffner 8r. Pearl 1992).sAlthough both types of approaches have provided use-sful techniques and insights we argue in this paper thatsa somewhat different treatment of priorities is needed.lsFor rea...

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...k, often much too weak (i.e., does not enable enough comparisons) to be a good candidate for preference representation, as it can be seen on the following example: let us consider the propositional language generated by two propositional variables a and b and let GB = { : a}. Then, for any x, y ∈ {(a, b), (a,¬b), (¬a, b), (¬a,¬b)}, x GB y holds if and only if x = y (and therefore x >GB y never holds). 3.3.4.2. Preference relation based on Z-ranking. While Rcond,S considered all models satisfying a set of conditionals, the approach based on the Z-completion of GB, at work in System-Z [45] and similar approaches, selects one model and allows much more consequences to be derived. Given a set GB = D of conditional rules φ : ψ and a set of hard facts, System-Z proceeds by partitioning D into a collection D0 ∪ · · · ∪ Dn; if a conditional rule ϕ : ψ is in Di then its rank is i. We omit to explain how the ranking is computed as this is only derivative for the purposes of the paper. Note that ranks intuitively respect specificity relations between rules, i.e., more specific rules are assigned higher ranks. Now, the ranking function on conditional rules induces a ranking function κ on...

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...t any revision process that satisfies natural requirements is implicitly based on such a set of priorities. Similarly a proper treatment of default rules also leads to prescribe priority levels (e.g. =-=Pearl, 1990-=-). In these two cases, the handling of priorities has been shown to be completely in agreement with possibilistic logic (Dubois, Lang and Prade, 1992b; Benferhat et al., 1992). Fox et al. (1992) also ...

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...lt thus provides added insight into and justification for approaches such as those of [Bacchus et al. 1993; Geffner 1992a; Goldszmidt and Pearl 1992; Goldszmidt et al. 1993; Lehmann and Magidor 1992; =-=Pearl 1990-=-] that, roughly speaking, say d follows from \Delta if d is true in a particular structure P \Delta 2 P that satisfies \Delta (rather than requiring that d be true in all structures in P that satisfy ...

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... P (P for preferential) proposed by Kraus, Lehmann and Magidor [32], which provides a very cautious inference system. In order to get a less conservative inference, Lehmann (see [36], [38]) and Pearl =-=[42] have prop-=-osed to add an inference rule, first suggested by Makinson, called rational monotony, and a particular entailment (named "rational closure entailment" [38]) has been defined which satisfies ...