Logical foundations of artificial intelligence
Logical foundations of artificial intelligence
Mathematical methods for artificial intelligence and autonomous systems
Mathematical methods for artificial intelligence and autonomous systems
The structure-mapping engine: algorithm and examples
Artificial Intelligence
CNLS '89 Proceedings of the ninth annual international conference of the Center for Nonlinear Studies on Self-organizing, Collective, and Cooperative Phenomena in Natural and Artificial Computing Networks on Emergent computation
Similarity and analogical reasoning
Similarity and analogical reasoning
The mechanisms of analogical learning
Similarity and analogical reasoning
Basic category theory for computer scientists
Basic category theory for computer scientists
Categories, types, and structures: an introduction to category theory for the working computer scientist
Categories and computer science
Categories and computer science
Analogy-making as perception: a computer model
Analogy-making as perception: a computer model
Case-based reasoning
Mental leaps: analogy in creative thought
Mental leaps: analogy in creative thought
Category theory for computing science, 2nd ed.
Category theory for computing science, 2nd ed.
The subtlety of sameness: a theory and computer model of analogy-making
The subtlety of sameness: a theory and computer model of analogy-making
Mathematical methods in artificial intelligence
Mathematical methods in artificial intelligence
From environments to representations—a mathematical theory of artificial perceptions
Artificial Intelligence
Being There: Putting Brain, Body, and World Together Again
Being There: Putting Brain, Body, and World Together Again
Case-Based Reasoning: Experiences, Lessons and Future Directions
Case-Based Reasoning: Experiences, Lessons and Future Directions
Fluid Concepts and Creative Analogies: Computer Models of the Fundamental Mechanisms of Thought
Fluid Concepts and Creative Analogies: Computer Models of the Fundamental Mechanisms of Thought
Introducing the mathematical category of artificial perceptions
Annals of Mathematics and Artificial Intelligence
Semantic Information Processing
Semantic Information Processing
| Hi-index | 0.01 |
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.