Towards an Algebraic Theory of Analogical Reasoning in Logic Programming

Analogy-making is an essential part of human intelligence and creativity. This paper proposes an algebraic model of analogical reasoning in logic programming based on the syntactic composition and decomposition of programs. The main idea is to define analogy in terms of modularity and to derive abstract forms of concrete programs from a `known' source domain which can then be instantiated in an `unknown' target domain to obtain analogous programs. To this end, we introduce algebraic operations for program modularity and illustrate, by giving numerous examples, that programs have nice decompositions. Interestingly, our work suggests a close relationship between modularity, generalization, and analogy which we believe should be explored further in the future. In a broader sense, this paper is a first step towards an algebraic (and mainly syntactic) theory of analogical reasoning in logic-based knowledge representation and reasoning systems, with potential applications to fundamental AI-problems like computational learning and creativity.