Approximation in Description Logics: How Weighted Tree Automata Can Help to Define the Required Concept Comparison Measures in \(\mathcal {FL}_0\)

Recently introduced approaches for relaxed query answering, approximately defining concepts, and approximately solving unification problems in Description Logics have in common that they are based on the use of concept comparison measures together with a threshold construction. In this paper, we will briefly review these approaches, and then show how weighted automata working on infinite trees can be used to construct computable concept comparison measures for \(\mathcal {FL}_0\) that are equivalence invariant w.r.t. general TBoxes. This is a first step towards employing such measures in the mentioned approximation approaches.