In this paper, we deal with the problem of debugging and revision of incoherent terminologies. Ontology debugging aims to provide the explanation of the causes of incoherence and ontology revision aims to eliminate the incoherence. For this purpose, we propose the graph-based approaches to deal with the debugging and revision of terminologies for a family of lightweight ontology languages, DL-Lite. First of all, we transform DL-Lite ontologies to graphs. To deal with the problem of ontology debugging, we calculate the minimal incoherence-preserving subsets (MIPS) of an ontology by computing the minimal incoherence-preserving path-pairs (MIPP) based on the transformed graph. To deal with the problem of ontology revision, we propose the notion of revision state which separates the terminology of an ontology into two disjoint sets: the set of wanted axioms and the set of unwanted axioms. We further define a revision operator based on the revision state. Afterward, two revision algorithms are proposed to instantiate the revision operator: one is based on a scoring function, and the other one is based on a hitting set tree. We implement these algorithms and conduct experiments of ontology debugging and ontology revision on several adapted real ontologies. The experimental results of ontology debugging show that our approach of calculating MIPS based on graph is efficient and outperforms the state of the art. The experimental results of ontology revision show that the algorithm based on a scoring function is more efficient than the algorithm based on a hitting set tree.

/pdf/graph-based-approaches-to-debugging-and-revision-of-3wf9t2lt9x.pdf

Graph-based approaches to debugging and revision of terminologies in DL-Lite

In this paper, we address the problem of applying AGM-style belief revision to non-classical logics. We discuss the idea of minimal change in revision and show that for non-classical logics, some sort of minimality postulate has to be explicitly introduced. We also present two constructions for revision which satisfy the AGM postulates and prove the representation theorems including minimality postulates.

/pdf/minimal-change-in-agm-revision-for-non-classical-logics-4x7ebvvacr.pdf

Minimal change in AGM revision for non-classical logics

Same as Dung's abstract argumentation framework (AF), the notion of generalized abstract argumen- tation framework (GenAF) aims at reasoning about inconsistency disregarding any logic for arguments; thus both the knowledge base (KB) and language to express beliefs remain unspecified. Nonetheless, reifying the abstract configuration of the AF argumentation machineries to specific logics may bring about some inconveniences. A GenAF is assumed to eventually relate first-order logic (FOL) formulae to abstract arguments. The main purpose of the generalization is to provide a theory capable of reasoning (following argumentation technics) about inconsistent knowledge bases (KB) expressed in any FOL fragment. Consequently, the notion of argument is related to a single formula in the KB. This allows to share the same primitive elements from both, the framework (arguments) and, the KB (formulae). A framework with such features would not only allow to manage a wide range of knowledge representation languages, but also to cope straightforwardly with the dynamics of knowledge. Once the formalism is presented, we propose a reification to the description logic ALC with the intention to handle ontology debugging. In this sense, since argumentation frameworks reason over graphs that relate arguments through attack, our methodology is proposed to bridge ontological inconsistency sources to attack relations in argumentation. Finally, an argumentation semantics adapted to GenAF's, is proposed as a consistency restoration tool with the objective of debugging and repairing ontologies.

Generalized Abstract Argumentation: A First-order Machinery towards Ontology Debugging

Datalog+/- is a family of emerging ontology languages that can be used for representing and reasoning over lightweight ontologies in Semantic Web. In this paper, we propose an approach to performing belief base revision for Datalog+/- ontologies. We define a kernel based belief revision operator for Datalog+/- and study its properties using extended postulates, as well as an algorithm to revise Datalog+/- ontologies. Finally, we give the complexity results by showing that query answering for a revised linear Datalog+/- ontology is tractable.

Belief Base Revision for Datalog+/- Ontologies

In this paper, we propose a service for contracting axioms from ontologies based on the description logic EL. In particular, we devise algorithms that implement the contraction operation of the AGM theory on belief change. We first generalise the AGM contraction postulates to description logics, in which a variant of the recovery postulate is defined by using the notion of logical difference. Plausibility of the contraction operation is demonstrated by showing that it satisfies all the generalised postulates.

/pdf/belief-contraction-in-the-description-logic-el-3k7l48z1ua.pdf

Belief Contraction in the Description Logic EL.

In this paper, we propose a new method for revising terminologies in description logic-based ontologies. Our revision method is a reformulation of the kernel revision operator in belief revision. We first define our revision operator for terminologies in terms of MIPS (minimal incoherence-preserving sub-terminologies), and we show that it satisfies some desirable logical properties. Second, two concrete algorithms are developed to implement the revision operator.

/pdf/a-kernel-revision-operator-for-terminologies-481skse4er.pdf

A Kernel Revision Operator for Terminologies

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A Kernel Revision Operator for Terminologies