Algebraic anti-unification

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.