Abstract
In this thesis we study KLM-style rational reasoning in defeasible Description Logics. We illustrate that many recent approaches to derive consequences under Rational Closure (and its stronger variants, lexicographic and relevant closure) suffer the fatal drawback of neglecting defeasible information in quantified concepts. We propose novel model-theoretic semantics that are able to derive the missing entailments in two differently strong flavours. Our solution introduces a preference relation to distinguish sets of models in terms of their typicality (amount of defeasible information derivable for quantified concepts). The semantics defined through the most typical (most preferred) sets of models are proven superior to previous approaches in that their entailments properly extend previously derivable consequences, in particular, allowing to derive defeasible consequences for quantified concepts. The dissertation concludes with an algorithmic characterisation of this uniform maximisation of typicality, which accompanies our investigation of the computational complexity for deriving consequences under these new semantics.
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Notes
For a detailed introduction to DLs we refer to [2].
These advanced closure operators are alleviating the drawback of Rational Closure known as inheritance blocking.
Formally, an inclusion \(BrokenWing\sqcap Fly\sqsubseteq \bot\) is required to imply inconsistency of tweety with Bird
Fly.Formally, the set of all typicality models is finite, hence there are no infinite chains through \(<_t\).
Fly.References
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This work was supported by the German Research Foundation (DFG) in GRK 1763—Quantitative Logics and Automata.
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Pensel, M. A Lightweight Defeasible Description Logic in Depth. Künstl Intell 34, 527–531 (2020). https://doi.org/10.1007/s13218-020-00644-z
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DOI: https://doi.org/10.1007/s13218-020-00644-z