Understanding one another: making out meanings with Boolean equations

Autonomous ai agents raise the issue of semantic interoperability between independently architectured and differently embodied intelligences. This article offers an approach to the issue with certain aspects that are close in spirit to the way humans make out meanings. Using a mathematical model of cognition, it is shown how agents with autonomously developed conceptualizations can bootstrap and unravel each other’s meanings ad hoc. The domain general methodology is based on the agents’ capability to deal with Boolean operations, and on the shared outside environment. No prior provisions are required. The formalized cognitive process consists of constructing, and solving, Boolean equations that are grounded in the shared environment. The process yields a testable conjecture about the grounded conceptual representation of the other, along with a testable conjectured translation that maps from that representation to one’s own.      

Perceive this as that – Analogies, artificial perception, and category theory

This paper formalizes and analyzes cognitive transitions between artificial perceptions that consist of an analogical or metaphorical transference of perception. The formalization is performed within a mathematical framework that has been used before to formalize other aspects of artificial perception and cognition. The mathematical infrastructure consists of a basic category of ‘artificial perceptions’. Each ‘perception’ consists of a set of ‘world elements’, a set of ‘connotations’, and a three valued (true, false, undefined) predicative connection between the two sets. ‘Perception morphisms’ describe structure preserving paths between perceptions. Quite a few artificial cognitive processes can be viewed and formalized as perception morphisms or as other categorical constructs. We show here how analogical transitions can be formalized in a similar way. A factorization of every analogical transition is shown to formalize metaphorical perceptions that are inspired by the analogy. It is further shown how structural aspects of ‘better’ analogies and metaphors can be captured and evaluated by the same categorical setting, as well as generalizations that emerge from analogies. The results of this study are then embedded in the existing mathematical formalization of other artificial cognitive processes within the same premises. A fallout of the rigorous unified mathematical theory is that structured analogies and metaphors share common formal aspects with other perceptually acute cognitive processes. This revised version was published online in June 2006 with corrections to the Cover Date.     

Introducing the mathematical category of artificial perceptions

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, concept (different from the sense in which computer vision/audio research takes the concept of perception). We propose and develop premises for a formal approach to a fundamental phenomenon in AI: the diversity of artificial perceptions. A mathematical substratum is proposed as a basis for a rigorous 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 a basis for a mathematical theory. This theory provides a way of extending and systematizing certain intuitive pre-theoretical conceptions about perception, about improving and/or completing an agent's perceptual grasp, about transition between various perceptions, etc. Some example applications of the theory are analyzed. This revised version was published online in June 2006 with corrections to the Cover Date.