Algebraic anti-unification

TL;DR

This paper introduces an algebraic (semantic) framework for anti-unification in general algebras, expanding beyond the traditional syntactic approach, with implications for similarity and analogy in AI.

Contribution

It pioneers an algebraic (semantic) theory of anti-unification, broadening the scope beyond syntactic methods in AI and theoretical computer science.

Findings

Proposes an algebraic framework for anti-unification

Links anti-unification to similarity and analogical reasoning

Sets foundation for future semantic approaches in AI

Abstract

Abstraction is key to human and artificial intelligence as it allows one to see common structure in otherwise distinct objects or situations and as such it is a key element for generality in AI. Anti-unification (or generalization) is \textit{the} part of theoretical computer science and AI studying abstraction. It has been successfully applied to various AI-related problems, most importantly inductive logic programming. Up to this date, anti-unification is studied only from a syntactic perspective in the literature. The purpose of this paper is to initiate an algebraic (i.e. semantic) theory of anti-unification within general algebras. This is motivated by recent applications to similarity and analogical proportions.