Concept Dissimilarity Based on Tree Edit Distances and Morphological Dilations

A number of similarity measures for comparing description logic concepts have been proposed. Criteria have been developed to evaluate a measure's fitness for an application. These criteria include on the one hand those that ensure compatibility with the semantics, such as equivalence soundness, and on the other hand the properties of a metric, such as the triangle inequality. In this work we present two classes of dissimilarity measures that are at the same time equivalence sound and satisfy the triangle inequality: a simple dissimilarity measure, based on description trees for the lightweight description logic ℇL; and an instantiation of a general framework, presented in our previous work, using dilation operators from mathematical morphology, and which exploits the link between Hausdorff distance and dilations using balls of the ground distance as structuring elements.

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