Reasoning about Typicality with Low Complexity Description Logics: The Logic $\mathcal{EL}^{+^\bot}{\bf T}$

Abstract

We present an extension of the low complexity Description Logic $\mathcal{EL}^{+^\bot}$ for reasoning about prototypical properties and inheritance with exceptions. We add to $\mathcal{EL}^{+^\bot}$ a typicality operator T, which is intended to select the “most normal” instances of a concept. In the resulting logic, called $\mathcal{EL}^{+^\bot}{\bf T}$, the knowledge base may contain subsumption relations of the form “T(C) is subsumed by P”, expressing that typical C-members have the property P. We show that the problem of entailment in $\mathcal{EL}^{+^\bot}{\bf T}$ is in co-NP by proving a small model result.