Grant: Discovery Grants Program - Individual

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. The main aim of my research is to study the algebraic and logical foundations of relational reasoning and to supplement it by statistical and information theoretic methods that enable it to function as a reliable tool of non-invasive data analysis. The main application areas are qualitative temporal and spatial reasoning, theories of visual perception with a particular emphasis on JJ Gibson's work, and the development of structural tools for diagnostic assessment.