Rough Set Semantics for Identity on the Web

ABSTRACT. Identity relations are at the foundation of many logic-based knowledge representations. We argue that the traditional notion of equality, based on Leibniz’ principle of indiscernability, is unsuited for many realistic knowledge representation settings. The classical interpretation of equality is simply too strong when the equality statements are re-used outside their original context.

The most prominent modern example of such re-use of knowledge across contexts is the Linked Open Data initiative, and the SemanticWeb in general. On the SemanticWeb, equality statements are used to interlink multiple descriptions of the same object, using owl:sameAs assertions. And indeed, many practical uses of owl:sameAs are known to violate the formal Leibniz-style semantics.

First, we survey the problems with the classical definition of identity, both in general, and on the Semantic Web in particular. In order to provide a more flexible semantics to identity, we then propose a method that assigns meaning to the subrelations of an identity relation using the predicates that are used in a knowledge-base. Using those indiscernabilitypredicates, we define upper and lower approximations of equality in the style of rought-set theory, resulting in a quality-measure for the identity relation.

We illustrate our approach on a realistic Semantic Web dataset, and we experimentally verify that our approach yields the intuitively desired results on this dataset.