Analogical proportions II
This work addresses the foundational challenge of formalizing analogical reasoning, a core aspect of human and artificial general intelligence, but it appears incremental as it builds on the author's prior framework.
The paper tackles the problem of developing a mathematical theory for analogical proportions, which are expressions like 'a is to b what c is to d', by extending an abstract algebraic framework within universal algebra, with the result that this framework has been successfully applied to logic program synthesis in AI.
Analogical reasoning is the ability to detect parallels between two seemingly distant objects or situations, a fundamental human capacity used for example in commonsense reasoning, learning, and creativity which is believed by many researchers to be at the core of human and artificial general intelligence. Analogical proportions are expressions of the form ``$a$ is to $b$ what $c$ is to $d$'' at the core of analogical reasoning. The author has recently introduced an abstract algebraic framework of analogical proportions within the general setting of universal algebra. It is the purpose of this paper to further develop the mathematical theory of analogical proportions within that framework as motivated by the fact that it has already been successfully applied to logic program synthesis in artificial intelligence.