Algebraic and logical methods for data analysis

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Most methods of knowledge-discovery and data mining assume parameters outside the observed data such as prior probabilities, belief functions or statistical distributions, the origin of which is not always clear or justifiable. On the other hand, there is a high demand for "non-invasive" methods of data analysis (such as rough sets, concept lattices, or knowledge structures) that take into account only the given data without stringent additional model assumptions. Using fewer model assumptions results in more generality, wider applicability, less decontextualization, and reduced costs and time. A powerful tool of non-invasive data analysis is relational reasoning, based on ideas developed by Alfred Tarski in the 1940s and which incorporate both relational and algebraic aspects of reasoning procedures.