Reasoning About Surprising Scenarios in Description Logics of Typicality

We continue our investigation on nonmonotonic procedures for preferential Description Logics in order to reason about plausible but surprising scenarios. We consider an extension ALC + T-R(exp) of the non-monotonic logic of typicality ALC + T-R by inclusions of the form T(C) subset of 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 ALC + T-R(exp) and we exploit it to show that entailment is in ExpTime as for the underlying 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.