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## Section: Research Program

Vast amounts of rdf data are made available on the web by various institutions providing overlapping information. To be fully exploited, different representations of the same object across various data sets, often using different ontologies, have to be identified. When different vocabularies are used for describing data, it is necessary to identify the concepts they define. This task is called ontology matching and its result is an alignment $A$, i.e. a set of correspondences $〈e,r,{e}^{\text{'}}〉$ relating entities $e$ and ${e}^{\text{'}}$ of two different ontologies by a particular relation $r$ (which may be equivalence, subsumption, disjointness, etc.) [4].

At the data level, data interlinking is the process of generating links identifying the same resource described in two data sets. Parallel to ontology matching, from two datasets ($d$ and ${d}^{\text{'}}$) it generates a link set, $L$ made of pairs of resource identifier.

We have introduced link keys [4], [1] which extend database keys in a way which is more adapted to rdf and deals with two data sets instead of a single relation. An example of a link key expression is:

$\begin{array}{c}\hfill \left\{〈\mathrm{𝖺𝗎𝗍𝖾𝗎𝗋},\mathrm{𝖼𝗋𝖾𝖺𝗍𝗈𝗋}〉\right\}\left\{〈\mathrm{𝗍𝗂𝗍𝗋𝖾},\mathrm{𝗍𝗂𝗍𝗅𝖾}〉\right\}\phantom{\rule{3.33333pt}{0ex}}linkkey\phantom{\rule{3.33333pt}{0ex}}〈\mathrm{𝖫𝗂𝗏𝗋𝖾},\mathrm{𝖡𝗈𝗈𝗄}〉\end{array}$

stating that whenever an instance of the class $\mathrm{𝖫𝗂𝗏𝗋𝖾}$ has the same values for the property $\mathrm{𝖺𝗎𝗍𝖾𝗎𝗋}$ as an instance of class $\mathrm{𝖡𝗈𝗈𝗄}$ has for the property $\mathrm{𝖼𝗋𝖾𝖺𝗍𝗈𝗋}$ and they share at least one value for their property $\mathrm{𝗍𝗂𝗍𝗋𝖾}$ and $\mathrm{𝗍𝗂𝗍𝗅𝖾}$, then they denote the same entity. More precisely, a link key is a structure $〈{K}^{eq},{K}^{in},C〉$ such that:

• ${K}^{eq}$ and ${K}^{in}$ are sets of pairs of property expressions;

• $C$ is a pair of class expressions (or a correspondence).

Such a link key holds if and only if for any pair of resources belonging to the classes in correspondence such that the values of their property in ${K}^{eq}$ are pairwise equal and the values of those in ${K}^{in}$ pairwise intersect, the resources are the same. Link keys can then be used for finding equal individuals across two data sets and generating the corresponding $\mathrm{𝗈𝗐𝗅}$:$\mathrm{𝗌𝖺𝗆𝖾𝖠𝗌}$ links. Link keys take into account the non functionality of rdf data and have to deal with non literal values. In particular, they may use arbitrary properties and class expressions. This renders their discovery and use difficult.