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The general purpose of this paper is to demonstrate through a well defined example how philosophy of science and Artificial Intelligence (AI) can benefit from each other by sharing some of their ideas, methods and techniques developed to tackle similar problems The problem we will focus is the expression of non-deductive inferences, which is performed in AI by the use of nonmonotonic logics, and in philosophy of science by the attempt of constructing inductive logics After analyzing to what extent one of the most wide spread nonmonotonic formalisms – default logic – can be taken as a logic of induction in the philosophical sense, and carefully considering the similarities and dissimilarities of the problems faced in these contexts, an expanded version of default logic, called by us a logic of logic of inductive implication, is introduced It is then shown how this new framework can be used to represent different types of inductive calculi that may be of relevance to AI.