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...{r(i) | R ′ �|= Gi} – discrimin ordering [5, 14, 43]: Let d(R, R ′ ) = min{r(i) | R�|=Gi & R ′ |=Gi}. R � dis GB R′ iff d(R, R ′ ) < d(R ′ , R) or {Gi | R |= Gi} = {Gi | R ′ |= Gi} – leximin ordering =-=[5, 58]-=-: 7 Let dk(R) = |{Gi | R |= Gi & r(i) = k}|. 6 We are using the convention min(∅) = +∞. 7 Not to be confused with (although related to) the leximin ordering for the aggregation of individual preferenc...

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...tions regarding the drowning problem. Some systematic methods for coping with this problem have been proposed, based on refined inconsistency handling (Geffner [27], Benferhat et al. [3],[6], Lehmann =-=[37])). B-=-ut they always face counter-examples and have high complexity [40], [10]. A more promising way of overcoming this problem may be to add information about conditional independence of the form &quot;in ...

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...bbases. Baral et al. (1992) have also used a similar approach to combine belief bases. The definition of Lex(��) has been proposed in another form in (Dubois et al., 1992a) and also independently =-=in (Lehmann, 1993). T-=-he idea of selecting a subset of the set of maximally consistent subbases of �� using a cardinality criterion was used independently in diagnostic problems (De Kleer, 1990; Lang, 1994). It corresp...

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...) and (σ) = i=1,...,n σ(i). • σi→j = 〈σ(i), . . . , σ(j)〉 for 1 ≤ i ≤ j ≤ n. 3 We find this view of a prior belief state as a list of input formulas in other works, e.g. (Konieczny & Pino-Pérez 2000; =-=Lehmann 1995-=-b). We shall return to this issue later. 213• If σ = 〈σ(1), . . . , σ(n)〉 and σ ′ = 〈σ′(1), . . . , σ ′(p)〉 then (σ, σ ′) (also sometimes denoted by σ.σ ′) is the concatenation of σ and σ ′, defined ...

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...homas Lukasiewicz from classes to exceptional subclasses, the maximum entropy approach to default entailment was proposed by Goldszmidt et al. [37]; lexicographic entailment was introduced by Lehmann =-=[55]-=- and Benferhat et al. [7]; conditional entailment was proposed by Geffner [32, 33]; and an infinitesimal belief function approach was suggested by Benferhat et al. [10]. In this paper, we combine the ...

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...nd + Z are incomparable. Another solution to get non-monotonic inferences that go beyond those of system P is to use the so-called lexicographic approach (Dubois et al., 1991, Benferhat et al., 1993, =-=Lehmann, 1993-=-). One well know drawback of this approach is that it is syntax-sensitive: repetitions of the same default in ∆ may change the result. We show that LCD is not sensitive to duplications. Example 7. Con...

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...a sequence (K; S 1 ; : : : ; S n ) of sets of classical propositional formulas. Since we need K to be a non-default level we slightly modify the denition of lexicographically preferred subbases from [=-=1,-=- 13]. Denition 10 Let KB = (K; S 1 ; : : : ; S n ) be a stratied knowledge base. A maximal consistent subset S of (K [ S 1 [ : : : [ S n ) is a lexicographically preferred subbase of KB i 1. K S, and...