Reasoning about plausible scenarios in Description Logics of typicality

Abstract

In some application domains it is sometimes useful to reason about plausible but “not obvious” scenarios, excluding the most trivial ones. In this work we introduce nonmonotonic procedures for preferential Description Logics in order to reason about plausible but – in some sense – “surprising” scenarios. We consider an extension, called $\mathcal{ALC}+T_R^{\exp }$, of the nonmonotonic logic of typicality $\mathcal{ALC}+T_R$ by inclusions of the form T (C) ⊑  _d D, where d is a degree of expectedness. We consider a notion of extension of an ABox, in order to assume typicality assertions about individuals satisfying cardinality restrictions on concepts, then we define a preference relation among such extended ABoxes based on the degrees of expectedness, then we restrict entailment to those extensions that are minimal with respect to this preference relation. We propose a decision procedure for reasoning in $\mathcal{ALC}+T_R^{\exp }$ and we exploit it to show that entailment is in ExpTime as for the underlying $\mathcal{ALC}$. Last, we introduce a further extension of the proposed approach in order to reason about all plausible extensions of the ABox, by restricting the attention to specific degrees of expectedness ranging from the most surprising scenarios to the most expected ones, and we show that entailment remains in ExpTime also in these cases.