Contextualizing DL Axioms: Formalization, a New Approach, and Its Properties

We address the problem of providing contextual information about a logical formula (e.g., provenance, date of validity, or confidence) and representing it within a logical system. In this case, it is needed to rely on a higher order or non standard formalism, or some kind of reification mechanism. We explore the case of reification and formalize the concept of contextualizing logical statements in the case of Description Logics. Then, we define several properties of contextualization that are desirable. No previous approaches satisfy all of the them. Consequently, we define a new way of contextually annotating statements. It is inspired by NdFluents, which is itself an extension of the 4dFluents approach for annotating statements with temporal context. In NdFluents, instances that are involved in a contextual statement are sliced into contextual parts, such that only parts in the same context hold relations to one another, with the goal of better preserving inferences. We generalize this idea by defining contextual parts of relations and classes. This formal construction better satisfies the properties, although not entirely. We show that it is a particular case of a general mechanism that NdFluents also instantiates, and present other variations.