A Well-founded Graph-based Summarization Framework for Description Logics
Résumé
The quotient operation from graph theory offers an elegant graph summarization framework that has been widely investigated in the literature, notably for the exploration and efficient management of large graphs; it consists in fusing equivalent vertices according to an equivalence relation. In this paper, we study whether a similar operation may be used to summarize ABoxes. Towards this goal, we define and examine the quotient operation on an ABox: we establish that a quotient ABox is more specific than the ABox it summarizes, and characterize to which extent it is more specific. This preliminary investigation validates the interest of a quotient-based ABox summarization framework, and paves the way for further studies on it in the description logic setting, e.g., to devise equivalence relations suited to the optimization of typical data management and reasoning tasks on large ABoxes or to the visualization of large ABoxes, and on its utilization in related settings, e.g., Semantic Web.
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