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...tain some inconsistent pieces of information may produce useful answers to queries. The obvious conclusion from this state of affairs is that a more appropriate logic is needed for such systems. Thus =-=[15]-=- says: Informally speaking, paraconsistency is the paradigm of reasoning in the presence of inconsistency. Classical logic intolerantly invalidates any useful reasoning if there is any inconsistency, ...

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...licting goals, and complex software specifications in which different stake-holders have incompatible requirements are just a few cases in point. Recently, suggestions have even been made (see, e.g., =-=[27]-=-) to adopt paraconsistent logic as a foundational concept for future information systems engineering. One of the oldest and best known approaches to paraconsistency is da Costa’s approach ([24, 25, 28...

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...not. However, standard resolution-based query answering (which is used for implementing the approach of [16] in [11]) can be characterised as a procedural form of paraconsistent reasoning (as done in =-=[10, 5, 6]-=-) that merits attention with regard to violation tolerance. It does not take irrelevant database clauses into account for evaluating constraints upon some update, even if such clauses would be involve...

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...hecking require that the database state before the update satisfies integrity. Only then, it is sufficient to evaluate simplified queries for ensuring integrity of the new state, after the update. In =-=[6]-=-, we have argued that it is possible to safely use well-known query valuation procedures also in the presence of inconsistent data and in particular in the presence of information that does not satisf...

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...hecking require that the database state before the update satisfies integrity. Only then, it is sufficient to evaluate simplified queries for ensuring integrity of the new state, after the update. In =-=[1]-=-, we have argued that it is possible to safely use well-known query evaluation procedures also 5 in the presence of inconsistent data and in particular in the presence of information that does not sat...

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... such as scientific and life science data management. Scientists usually do not prefer to use default negation rules to infer negative data and rely on the open world assumption. Several researchers (=-=[5, 7, 11]-=-) have looked into the problem of representing and manipulating negative data explicitly in databases. Such databases have been referred to as paraconsistent databases as they are based on 4-valued pa...

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... iff aI = a for every DBox individual a ∈∑I and for every concept or role name P ∈∑D(P ) and for every u ∈ ∆I and respectively (u, v) ∈ ∆I × ∆I iff P (u) ∈ D and respectively (u, v) ∈ PI, P (u, v) ∈ D=-=[2]-=-[6]. We can say that every model of D extension attached to DBox predicate, identified by:∑ D (P ) = ∑ D (C) ⋃∑ D (R) (7) is given by the content of DBox and is the same in every model. We must mentio...