Representing Uncertain Concepts in Rough Description Logics via Contextual Indiscernibility Relations

Abstract

We investigate the modeling of uncertain concepts via rough description logics (RDLs), which are an extension of traditional description logics (DLs) by a mechanism to handle approximate concept definitions via lower and upper approximations of concepts based on a rough-set semantics. This allows to apply RDLs to modeling uncertain knowledge. Since these approximations are ultimately grounded on an indiscernibility relation, we explore possible logical and numerical ways for defining such relations based on the considered knowledge. In particular, we introduce the notion of context, allowing for the definition of specific equivalence relations, which are directly used for lower and upper approximations of concepts. The notion of context also allows for defining similarity measures, which are used for introducing a notion of tolerance in the indiscernibility. Finally, we describe several learning problems in our RDL framework.