Section: New Results

Link keys

Link keys (§3.2) are explored following two directions:

• Extracting link keys;

• Reasoning with link keys.

Link key extraction with relational concept analysis

Participants : Manuel Atencia, Jérôme David [Correspondent] , Jérôme Euzenat.

We first described our extraction approach [1] in the framework of formal context analysis (FCA, [20]). We recently showed that link keys extracted by formal concept analysis are equivalent to an extension of those which were extracted by our former algorithm [15]. We also used pattern structures, an extension of FCA with ordered structures, to reformulate this problem [6].

Furthermore, we used relational concept analysis (RCA, [22]), an extension of FCA taking relations between concepts into account. We showed that it is possible to encode the link key extraction problem in RCA to extract the optimal link keys even in the presence of cyclic dependencies [5]. Moreover, the proposed process does not require information about the alignments between the ontologies to find out from which pairs of classes to extract link keys.

We implemented these methods and evaluated them by reproducing the experiments made in previous studies. This shows that the method extracts the expected results as well as (also expected) scalability issues.

Combining link keys

Participants : Manuel Atencia, Alice Caporali, Jérôme David [Correspondent] , Jérôme Euzenat, Basile Legal.

For certain data sets, it may be necessary to use several link keys, even on the same pair of classes, for retrieving a more complete link set. We introduced operators to combine link keys over the same pair of classes, investigated their relations and extended measures to evaluate their quality.

We specifically proposed strategies to extract disjunctions from RDF data and apply existing quality measures to evaluate them. We experimented with these strategies showing their benefits [7].

Tableau method for $\mathrm{𝒜ℒ𝒞}+$Link key reasoning

Participants : Manuel Atencia [Correspondent] , Jérôme Euzenat, Khadija Jradeh.

Link keys can also be thought of as axioms in a description logic. As such, they can contribute to infer ABox axioms, such as links, terminological axioms, or other link keys. This has important practical applications, such as link key inference, link key consistency and link key redundancy checking. Yet, no reasoning support existed for link keys.

We previously extended the tableau method designed for the $\mathrm{𝒜ℒ𝒞}$ description logic to support reasoning with link keys in $\mathrm{𝒜ℒ𝒞}$. We showed how this extension enables combining link keys with classical terminological reasoning with and without ABox and TBox and generating non-trivial link keys. We further extended the method and have proven that this extended method terminates, is sound, complete, and that its complexity is 2ExpTime [11].

This work is part of the PhD thesis of Khadija Jradeh, co-supervised with Chan Le Duc (LIASD).