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The result is a powerful theory with applications in many areas of mathematics.

In Higher Topos Theory, Jacob Lurie presents the foundations of this theory, using the language of weak Kan complexes introduced by Boardman and Vogt, and shows how existing theorems in algebraic topology can be reformulated and generalized in the theory's new language. Higher category theory is generally regarded as technical and forbidding, but part of it is considerably more tractable: the theory of infinity-categories, higher categories in which all higher morphisms are assumed to be invertible. It results from the integration of background knowledge with new insights extracted from data models, generated for specific data modelling tasks, and represented as rules using the sketches language. The system is a data mining collaborative workplace, where the Information System knowledge base is an algebraic structure. It is the result of applying the graphic logic based language of sketches to knowledge integration. The Actias system is our approach to this paradigm. This paradigm is centred on a collaborative data mining strategy, where groups of experts collaborate using data-mining process on the supervised acquisition of new knowledge extracted from heterogeneous machine learning data models. We attempt to solve the knowledge acquisition problem, for a Business Information System, developing a supervised multistrategy learning paradigm.

As a consequence, the rate of progress in the development of this type of system is directly related to the speed with which knowledge bases can be assembled, and on its quality. One of the most difficult problems in the development of intelligent systems is the construction of the underlying knowledge base.

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