
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 " transforms into as transforms into " 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,…
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Taxonomy
TopicsLogic, Reasoning, and Knowledge · Logic, programming, and type systems · AI-based Problem Solving and Planning
