Logic Program Proportions

Analogy-making is at the core of human intelligence and creativity with applications to such diverse tasks as commonsense reasoning, learning, language acquisition, and story telling. This paper contributes to the foundations of artificial general intelligence by developing an abstract algebraic framework for logic-based analogical reasoning and learning in the setting of logic programming. The main idea is to instantiate the abstract algebraic framework of analogical proportions of the form $a:b::c:d$, recently introduced by the author, in the domain of logic programming. That is, in this paper we introduce and study logic program proportions of the form $P:Q::R:S$ as a mechanism for learning similar programs by analogy-making. Technically, we define proportions in terms of modularity where we 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 syntactic logic program composition and concatenation. We then argue that reasoning and learning by analogy is the task of solving analogical equations between logic programs. 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 further step towards an algebraic and mainly syntactic theory of logic-based analogical reasoning and learning in knowledge representation and reasoning systems, with potential applications to fundamental AI-problems like commonsense reasoning and computational learning and creativity.