Nonmonotonic reasoning, preferential models and cumulative logics
Artificial Intelligence
Description logics of minimal knowledge and negation as failure
ACM Transactions on Computational Logic (TOCL)
Reasoning about Typicality in Preferential Description Logics
JELIA '08 Proceedings of the 11th European conference on Logics in Artificial Intelligence
Prototypical Reasoning with Low Complexity Description Logics: Preliminary Results
LPNMR '09 Proceedings of the 10th International Conference on Logic Programming and Nonmonotonic Reasoning
Default inheritance reasoning in hybrid KL-ONE-style logics
IJCAI'93 Proceedings of the 13th international joint conference on Artifical intelligence - Volume 1
IJCAI'05 Proceedings of the 19th international joint conference on Artificial intelligence
Defeasible inclusions in low-complexity DLs: preliminary notes
IJCAI'09 Proceedings of the 21st international jont conference on Artifical intelligence
Preferential description logics
LPAR'07 Proceedings of the 14th international conference on Logic for programming, artificial intelligence and reasoning
A non-monotonic Description Logic for reasoning about typicality
Artificial Intelligence
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We present an extension of the low complexity Description Logic $\mathcal{EL}^{+^\bot}$ for reasoning about prototypical properties and inheritance with exceptions. We add to $\mathcal{EL}^{+^\bot}$ a typicality operator T, which is intended to select the "most normal" instances of a concept. In the resulting logic, called $\mathcal{EL}^{+^\bot}{\bf T}$, the knowledge base may contain subsumption relations of the form "T(C ) is subsumed by P ", expressing that typical C -members have the property P . We show that the problem of entailment in $\mathcal{EL}^{+^\bot}{\bf T}$ is in co-NP by proving a small model result.