We are interested in learning from examples and problem solving in an evolutive universe represented by an incomplete knowledge base. We formalize a knowledge representation framework that could be built and criticized by human and/or artificial agents. This knowledge representation is called a semi-empirical theory because this kind of theory is not completely axiomatic. We formalize a system called a mental scheme modelling the knowledge increase during the learning process. We deal with the dynamic characteristic of the learning acquisition process through reasoning mechanisms, proof building and the definition of a knowledge core.
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