From Environments to Representations - A Mathematical Theory of Artificial Perceptions

Abstract Perception is the recognition of elements and events in the environment, usually through integration of sensory impressions. It is considered here as a broad, high-level, object centered, phenomenon which happens at and above the level of holistic recognition of objects and events, where semantics begin to play a role. We propose and develop a mathematical theory of artificial perceptions. A basic mathematical category is defined. Its objects are perceptions, consisting of world elements, connotations, and a three-valued true, false, undefined predicative correspondence between them. Morphisms describe paths between perceptions. This structure serves as premises for a mathematical theory. The theory provides rigorous tools of scrutiny that deal with fundamental issues of AI such as the diversity and embodiment of artificial perceptions. It extends and systematizes certain intuitive pre-theoretical conceptions about perception, about improving and/or completing an agent's perceptual grasp, about transition between various perceptions, etc. Mathematical tools and methods are used to formalize reasonable ways to go about producing a meaningful cognitive image of the environment from every perception.