Logic program proportions

TL;DR

This paper proposes a novel approach to symbolic learning through analogical reasoning by defining directed analogical proportions between logic programs, aiming to develop a mathematical theory for logic-based analogy and learning.

Contribution

It introduces a formal framework for analogical proportions in logic programming using algebraic operations, linking modularity, generalization, and analogy.

Findings

Defined proportions in terms of modularity for logic programs

Established algebraic operations for program composition and concatenation

Suggested a close relationship between modularity, generalization, and analogy

Abstract

The purpose of this paper is to present a fresh idea on how symbolic learning might be realized via analogical reasoning. For this, we introduce directed analogical proportions between logic programs of the form "$P$ transforms into $Q$ as $R$ transforms into $S$" as a mechanism for deriving similar programs by analogy-making. The idea is to instantiate a fragment of a recently introduced abstract algebraic framework of analogical proportions 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 a mathematical theory of logic-based analogical reasoning and learning with potential applications to open AI-problems like commonsense reasoning and computational learning and creativity.