Directed 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 studies directed analogical proportions between logic programs of the form `$P$ transforms into $Q$ as $R$ transforms into $S$' -- in symbols, $P\dashrightarrow Q::R\dashrightarrow S$ -- as a mechanism for deriving similar programs by analogy-making. The idea is to instantiate an abstract algebraic framework of analogical proportions recently introduced by the author in the domain of logic programming. 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. 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 theory of logic-based analogical reasoning and learning with potential applications to fundamental AI-problems like commonsense reasoning and computational learning and creativity.