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...termination [8], there are some new non-trivial problems to be solved. To overcome the problem of having to design a new pinpointing extension for every tableau-based algorithm, we have introduced in =-=[5]-=- a general approach for extending tableau-based algorithms to pinpointing algorithms. This approach has, however, some annoying limitations. First, it only applies to tableau-based algorithms that ter...

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...proaches for reasoning in possibilistic Description Logics [15, 13] (where the lattice is the interval [0, 1] with the usual order) and glass-box approaches to axiom pinpointing in Description Logics =-=[19, 14, 12, 3, 4]-=- (where the lattice consists of (equivalence classes of) monotone Boolean formulae with implication as order [4]). The problem with glass-box approaches is that they 3 Figure 1 in Section 3 shows a sm...

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... [2]. In order to overcome the problem of developing a pinpointing extension for every particular tableau-based algorithm, a general pinpointing extension for tableau algorithms has been developed in =-=[3,6]-=-. Similarly, an automata-based general approach for obtaining glass-box pinpointing algorithms has been introduced in [4,5]. In contrast to the glass-box approach, the idea underlying the black-box ap...

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... changed to `g. Such a set will be called a change set. In order to commit as least changes as possible, we will prefer change sets of smaller cardinality. We show that the ideas of axiom pinpointing =-=[13, 12, 11, 4, 3]-=- can be adapted to the search of a change set with minimum cardinality. We present black-box methods, improving upon the Hitting Set Tree approach to axiom pinpointing [10, 14] that yield the desired ...

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...nts set by domain users, most logic-based applications provide explanation algorithms for reasoning services. This holds also for DLs, where research focused on the explanation of both TBox reasoning =-=[12,6,14,3]-=- and, more recently, query answering [5]. In addition, the latter paper advocates the importance of tackling the problem of explaining the absence of a tuple in the answers to a query over an ontology...

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...has been introduced in our prior work in [10, 9]. For every CS S ⊆ O there is a MCS M := {(a, `g) | a ∈ S} and lblM (c) = `g holds. The computation of a CS exploited main ideas from axiom-pinpointing =-=[8, 2]-=- and we presented a black-box approach that yields the desired set. Intuitively, a consequence c needs to be made more public if `g > lbl(c) or less public if `g < lbl(c). From the perspective of the ...

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...are based on a black-box approach, in which an unmodified reasoner is called repeatedly until the boundary has been found. In fact, attempts to produce a glass-box approach for e.g. axiom-pinpointing =-=[4]-=-, where the reasoner is modified to directly computethe boundary, encounter the problem that most of the optimizations used in implemented DL reasoners do not work in the modified procedures, making ...