Abstract: This paper addresses methods of specialising rst-order theories within the context of incremental learning systems. We demonstrate the shortcomings of existing rst-order incremental learning systems with regard to their specialisation mechanisms. We prove that these shortcomings are fundamental to the use of classical logic. In particular, minimal \\correct-ing\" specialisations are not always obtainable within this framework. We propose instead the adoption of a specialisation scheme based on an existing non-monotonic logic formalism. This approach overcomes the problems that arise with incremental learning systems which employ classical logic. As a side-eeect of the formal proofs developed for this paper we deene a function called \\deriv\" which turns out to be an improvement on an existing explanation-based-generalisation (EBG) algorithm. Prolog code and a description of the relationship between \\deriv\" and the previous EBG algorithm are described in an appendix.