An ASP Translation for Non-Monotonic Reasoning on DL-Liteℛ with Prototype Descriptions

In Artificial Intelligence, defeasible reasoning has been studied as one of the key features of common-sense
reasoning and consequently various kinds of non-monotonic logics have been developed to model it formally.
We recently developed a non-monotonic logic in the Description Logic (DL) framework based on a combination
of ideas from prototype theory, weighted DLs (aka “tooth logic”), and earlier work on justifiable exceptions. A
central ingredient in the new framework is the notion of a prototype description, weighted characterisations
of concepts denoting the typical features of its members. In this paper, we develop an initial ASP translation
for this system which allows to reason on instance level queries in the preferred models of a knowledge base.
In particular, under reasonable conditions on the form of the input knowledge base, we show that preference
reasoning on answer sets can be encoded via standard ASP constructs. We show that the translation is complete
with respect to the preferential semantics of our system.