Optimizing the computation of overriding in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.svg"><mml:msup><mml:mrow><mml:mi mathvariant="script">DL</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant="sans-serif">N</mml:mi></mml:mrow></mml:msup></mml:math>

One of the factors that is hindering adoption nonmonotonic description logics in applications performance. Even when monotonic and inferences have same asymptotic complexity, implementation reasoning may be significantly slower. This happens also with family DLN. In this work we address issue by introducing two optimizations for The first optimization, called optimistic evaluation, aims at exploiting incremental a better way. second module extractor DLN, has purpose focusing on relevant subset knowledge base. proposed optimization iterates that, unlike classical extractors, not idempotent, general. We prove are correct complete, assess them through extensive experiments. Our results optimized DLN often compatible interactive query answering, which brings closer to practical applications.