Perceive This as That { Analogical Cognitive Transitions with Categorical Tools

This paper formalizes and analyzes cognitive transitions between ar-tiicial perceptions that consist of an analogical or metaphorical transfer-ence of perception. The formalization is performed within a mathematical framework that has been used before to formalize other aspects of artii-cial perception and cognition. The mathematical infrastructure consists of a basic category ofàrtiicial perceptions'. Each`perception' consists of a set of`world elements', a set of`connotations', and a three valued (true, false, undeened) predicative connection between the two sets. `Percep-tion morphisms' describe structure preserving paths between perceptions. Quite a few artiicial cognitive processes can be viewed and formalized as perception morphisms. We show here how analogical transitions can also be formalized by perception morphisms. A factorization of every ana-logical transition is shown to formalize metaphorical transitions that are inspired by the analogy. It is further shown how structural aspects of`bet-ter' analogies and metaphors can be captured and evaluated by the same categorical setting. The results of this study are then embedded in the existing mathematical formalization of other artiicial cognitive processes within the same premises. A fallout of the rigorous uniied mathematical theory is that valid and complete artiicial perceptions warrant the most structured analogies and metaphors.