Abstract
We extend description logics (DLs) with non-monotonic reasoning features. We start by investigating a notion of defeasible subsumption in the spirit of defeasible conditionals as studied by Kraus, Lehmann and Magidor in the propositional case. In particular, we consider a natural and intuitive semantics for defeasible subsumption, and investigate KLM-style syntactic properties for both preferential and rational subsumption. Our contribution includes two representation results linking our semantic constructions to the set of preferential and rational properties considered. Besides showing that our semantics is appropriate, these results pave the way for more effective decision procedures for defeasible reasoning in DLs. Indeed, we also analyse the problem of non-monotonic reasoning in DLs at the level of entailment and present an algorithm for the computation of rational closure of a defeasible ontology. Importantly, our algorithm relies completely on classical entailment and shows that the computational complexity of reasoning over defeasible ontologies is no worse than that of reasoning in the underlying classical DL ALC.
Abstract (translated)
我们用非单调推理特性扩展了描述逻辑（DLS）。我们首先研究可撤销条件论精神中的可撤销的包容概念，正如克劳斯、莱曼和麦吉多在命题案例中所研究的那样。特别地，我们考虑了可撤销假设的自然和直观语义，并研究了优先和合理假设的KLM风格句法性质。我们的贡献包括两个表示结果，将我们的语义结构与所考虑的优先和合理属性集联系起来。这些结果不仅表明我们的语义是适当的，而且为DLS中不可撤销推理的更有效的决策过程铺平了道路。事实上，我们还分析了DLS在蕴涵层次上的非单调推理问题，并提出了一种计算可撤销本体的有理闭包的算法。重要的是，我们的算法完全依赖于经典蕴涵，并且表明可撤销本体上推理的计算复杂性并不比底层经典dl-alc中推理的计算复杂性差。
URL
https://arxiv.org/abs/1904.07559
