The paper attempts to give a formal framework to capture the entire process of scientific discovery including hypothesis formation, reasoning, identifying contradictions, peer reviewing, reformulating and so on. Data mining can be seen as one step in this complex process of interactive learning of an empirical theory This paper uses the terminology from paraconsistent logic and paracomplete logic that extends Aristotle square in a hypercube of oppositions which defines or substantiates any step of the discovery process. The central formal notions are validated on a mathematical scientific discovery game, and an industrial application in the field of Drug Discovery illustrates how the presented framework combines different learning processes to predict pharmaco-kinetic properties (ADME-T) and adverse side effects of therapeutic drug molecules. Index Terms—Machine Learning, Scientific Method, Logical Reasoning Framework, Aristotle's Square of Oppositions