Algebraic anti-unification
This work addresses a foundational gap in AI and theoretical computer science by introducing a semantic approach to abstraction, which could impact various AI-related problems.
The paper tackles the problem of anti-unification being studied only syntactically by initiating an algebraic theory of anti-unification in general algebras, motivated by applications to similarity and analogical proportions.
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.