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...n that lists predicates (i.e., concept and role 400 names) to be minimized: in models of the cKB, the extension of these predicates is required to be minimal w.r.t. set inclusion. Following McCarthy (=-=McCarthy 1986-=-), the minimized predicates will usually be “abnormality predicates” identifying instances that are not typical for their class. When minimizing predicates, circumscription patterns can require other ...

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...ments that are named by an individual constant, as adopted by other non-monotonic DLs. Introduction Description Logics (DLs) are descendents of frame based systems and semantic networks (Minsky 1975; =-=Quillian 1968-=-). Their main improvement upon these early ancestors is that DLs are equipped with a formal semantics and with well-defined reasoning services that are decidable. To achieve decidability, the expressi...

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...Figure 2: Multiple exceptions and specificity default rules as proposed by Brewka (Brewka 1994), but different from standard prioritized circumscription which assumes a total ordering (McCarthy 1986; =-=Lifschitz 1985-=-). More information can be found in (Baader & Hollunder 1995b). We now introduce circumscription patters, which describe how individual predicates are treated during minimization. Definition 1 (Circum...

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...lt logic and on epistemic operators (Baader & Hollunder 1995a; 1995b; Straccia 1993; Donini, Nardi, & Rosati 1997; 2002; Donini et al. 1998; Padgham & Zhang 1993; Lambrix, Shahmehri, & Wahlloef 1998; =-=Eiter et al. 2004-=-; Rosati 2005). However, identifying a non-monotonic DL that is of sufficient expressivity and computationally well-behaved is a non-trivial task. In particular, the resulting formalisms often suffer ...

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...s, the heart is located on the right-hand side of the body”. There have been many proposals to extend DLs with non-monotonic features, based e.g. on Reiter’s default logic and on epistemic operators (=-=Baader & Hollunder 1995-=-a; 1995b; Straccia 1993; Donini, Nardi, & Rosati 1997; 2002; Donini et al. 1998; Padgham & Zhang 1993; Lambrix, Shahmehri, & Wahlloef 1998; Eiter et al. 2004; Rosati 2005). However, identifying a non-...

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...User Staff v ∃hasAccessTo.ConfidentialFile unionsq AbStaff BlacklistedStaff v Staff u ¬∃hasAccessTo.ConfidentialFile Figure 2: Multiple exceptions and specificity default rules as proposed by Brewka (=-=Brewka 1994-=-), but different from standard prioritized circumscription which assumes a total ordering (McCarthy 1986; Lifschitz 1985). More information can be found in (Baader & Hollunder 1995b). We now introduce...

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...s, the heart is located on the right-hand side of the body”. There have been many proposals to extend DLs with non-monotonic features, based e.g. on Reiter’s default logic and on epistemic operators (=-=Baader & Hollunder 1995-=-a; 1995b; Straccia 1993; Donini, Nardi, & Rosati 1997; 2002; Donini et al. 1998; Padgham & Zhang 1993; Lambrix, Shahmehri, & Wahlloef 1998; Eiter et al. 2004; Rosati 2005). However, identifying a non-...

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...umscription if the empty relation is used for ≺. Technically, partially ordered circumscription lies in between prioritized circumscription (McCarthy 1986; Lifschitz 1985) and nested circumscription (=-=Lifschitz 1995-=-). It extends prioritized circumscription by admitting partial orders and, compared to nested circumscription, has the advantage of being technically simpler while still offering sufficient expressive...

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... the formalization of biomedical ontologies such as GALEN (Rector & Copyright c© 2006, American Association for Artificial Intelligence (www.aaai.org). All rights reserved. Horrocks 1997) and SNOMED (=-=Cote et al. 1993-=-), and it has recently been argued by Rector et al. in (Rector 2004; Stevens et al. 2005) that such ontologies have to support defeasible inheritance to represent knowledge such as “in humans, the hea...

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...ght-hand side of the body”. There have been many proposals to extend DLs with non-monotonic features, based e.g. on Reiter’s default logic and on epistemic operators (Baader & Hollunder 1995a; 1995b; =-=Straccia 1993-=-; Donini, Nardi, & Rosati 1997; 2002; Donini et al. 1998; Padgham & Zhang 1993; Lambrix, Shahmehri, & Wahlloef 1998; Eiter et al. 2004; Rosati 2005). However, identifying a non-monotonic DL that is of...

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...understand. It is surprising that, although circumscription is one of the main approaches to non-monotonic reasoning, DLs based on circumscription have hardly received any attention. After the early (=-=Brewka 1987-=-; Cadoli, Donini, & Schaerf 1990) there appears to be no publication devoted to the subject. In this paper, we propose non-monotonic description logics based on circumscription and investigate their c...

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...orithms that underly state-of-the-art DL reasoners (Baader & Sattler 2000). It seems that existing sequent calculi for (propositional) circumscription and minimal entailment (Bonatti & Olivetti 2002; =-=Olivetti 1992-=-) could provide a starting point. – It seems necessary to develop a design methodology for modelling defeasible inheritance. The examples given in this paper indicate that the main challenge is to fin...

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... DLs investigated in this paper deserves being studied. For example, it is known that circumscription is slightly less expressive than default logic and autoepistemic logic in the propositional case (=-=Bonatti & Eiter 1996-=-). Still, for certain applications our logics are more powerful than the nonmonotonic DLs based on default logic in (Baader & Hollunder 1995a) since the latter impose drastic restrictions on expressiv...

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...nsions of the tableau algorithms that underly state-of-the-art DL reasoners (Baader & Sattler 2000). It seems that existing sequent calculi for (propositional) circumscription and minimal entailment (=-=Bonatti & Olivetti 2002-=-; Olivetti 1992) could provide a starting point. – It seems necessary to develop a design methodology for modelling defeasible inheritance. The examples given in this paper indicate that the main chal...

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...ch that, for some truth value assignment t to the Boolean variables, the graph t(G) obtained from G by including only those edges whose label evaluate to true under t is not 3-colorable. As shown in (=-=Stewart 1991-=-), co-CERT3COL is complete for NPNP. To obtain a problem complete for NEXPNP, Eiter et al. use the complexity upgrade technique: by encoding the input in a succinct form using Boolean circuits, the co...

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...to domain elements that are named by an individual constant, as adopted by other non-monotonic DLs. Introduction Description Logics (DLs) are descendents of frame based systems and semantic networks (=-=Minsky 1975-=-; Quillian 1968). Their main improvement upon these early ancestors is that DLs are equipped with a formal semantics and with well-defined reasoning services that are decidable. To achieve decidabilit...

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...s with non-monotonic features, based e.g. on Reiter’s default logic and on epistemic operators (Baader & Hollunder 1995a; 1995b; Straccia 1993; Donini, Nardi, & Rosati 1997; 2002; Donini et al. 1998; =-=Padgham & Zhang 1993-=-; Lambrix, Shahmehri, & Wahlloef 1998; Eiter et al. 2004; Rosati 2005). However, identifying a non-monotonic DL that is of sufficient expressivity and computationally well-behaved is a non-trivial tas...

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...is undecidable. This even holds in the case of empty TBoxes. The proof is by a reduction of the semantic consequence problem of modal logic on transitive frames, which has been proved undecidable in (=-=Chagrov 1994-=-). A frame is a structure F = (∆F, rF), where F a non-empty domain, r a role name, and rF ⊆ ∆F ×∆F. A pointed frame is a pair (F, d) such that d ∈ ∆F. For F = (∆F, rF) a frame, d, e ∈ ∆F, and n ∈ N, w...

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...oposals to extend DLs with non-monotonic features, based e.g. on Reiter’s default logic and on epistemic operators (Baader & Hollunder 1995a; 1995b; Straccia 1993; Donini, Nardi, & Rosati 1997; 2002; =-=Donini et al. 1998-=-; Padgham & Zhang 1993; Lambrix, Shahmehri, & Wahlloef 1998; Eiter et al. 2004; Rosati 2005). However, identifying a non-monotonic DL that is of sufficient expressivity and computationally well-behave...