Functional Calculus of Concepts for Knowledge Acquisition and Processing

摘要

This paper addresses the problem of formal representation of categorization and concept learning from logical perspective. That way, we construct functional calculus of concepts (FCC) as a natural deduction system enriched with subscripts and type assignments and based on identity. The idea of this presentation stems from our previous research in areas of Intentional Theory of Concepts and formal consideration of Aristotel's paradeigma (example). The first section clarifies the motivation and briefly outlines the guiding ideas of our approach in the broader context of related work. The second section starts with the discussion of Aristotel's ideas of example-based reasoning in connection with first principle grasping. We consider some relevant modern findings to support the claim that categorization and concept learning are based on identity rather then on similarity and comparison. That is the third section, which introduces the very functional calculus of concepts formalizing that way an Aristotelian paradeigma as a procedure of new concepts formation. The conclusion contains closing remarks and indicates directions for future work.