  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.
