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Automatic construction of implicative theories for mathematical domains

According to Wikipedia, logic can be considered as “the use and study of valid reasoning”. In mathematics and computer sciences one is usually interested in formal logic, i.e. “the study of inference with purely formal content. An inference possesses a purely formal content if it can be expressed as a particular application of a wholly abstract rule, that is, a rule that is not about any particular thing or property.” The formality of the content under logical consideration allows one for examining the reasoning without references to particular entities. Hence, formal logic offers a uniform approach to reasoning in all possible domains.