Rational Closure in SHIQ
This work addresses a theoretical problem in knowledge representation for AI, specifically in non-monotonic reasoning, but it is incremental as it builds on existing rational closure concepts.
The paper tackles the problem of defining rational closure for the logic SHIQ, which lacks the finite model property, by providing a semantic characterization based on preferential semantics and a finite rank approach. It shows that the rational closure of a TBox can be computed in EXPTIME using entailment in SHIQ.
We define a notion of rational closure for the logic SHIQ, which does not enjoys the finite model property, building on the notion of rational closure introduced by Lehmann and Magidor in [23]. We provide a semantic characterization of rational closure in SHIQ in terms of a preferential semantics, based on a finite rank characterization of minimal models. We show that the rational closure of a TBox can be computed in EXPTIME using entailment in SHIQ.