Axiomatizing ε L ⊥-expressible terminological knowledge from erroneous data

Abstract

In a recent approach, Baader and Distel proposed an algorithm to axiomatize all terminological knowledge that is valid in a given data set and is expressible in the description logic EL K . This approach is based on the mathematical theory of formal concept analysis. However, this algorithm requires the initial data set to be free of errors, an assumption that normally cannot be made for real-world data. In this work, we propose a first extension of the work of Baader and Distel to handle errors in the data set. The approach we present here is based on the notion of confidence, as it has been developed and used in the area of data mining.

Mining ℰℒ⊥ Bases with Adaptable Role Depth

“…This work extends our conference paper (Guimarães, Ozaki, Persia, & Sertkaya, 2021) with full proofs of the results presented there and with a section on compact representation of the product graph. In addition to these we extend our results to the case of mining a base from noisy data as suggested in (Borchmann, 2014). To this purpose, we show that our approach of adaptable role depth easily extends to CIs with a certain confidence threshold.…”

“…An approach for analysing data in an RDF-triple store using FCA to identify clusters has been proposed by Dau and Sertkaya (2011). In his dissertation, Borchmann (2014) considers noisy data and shows how a base of confident EL ⊥ gf p concept inclusions can be extracted from a DL interpretation by extending Distel's work. Borchmann et al (2016) address the problems with the fixpoint semantics of EL ⊥ gf p .…”

“…We investigate an extension of our framework to the case where the goal is to obtain a base with GCIs that may only partially match the finite interpretation, as originally considered by Borchmann (2013aBorchmann ( , 2013bBorchmann ( , 2014 for EL ⊥ gf p GCIs. The goal of such approach is to cope with noisy data.…”

“…Definition 9 (Confidence of GCIs (Borchmann, 2014)). Let I = (∆ I , • I ) be a finite interpretation over N C and N R , and let C, D be EL ⊥ concept expressions.…”

“…Lemma 8 (Lemma 5.2.12 in (Borchmann, 2014)). Let (∆ I , • I ) be a finite interpretation, and let Z ⊆ Y ⊆ X.…”