… This paper considers the problem of E-unification for arbitrary equational theories E, and
presents an inference rule approximating Paramodulation and leading to a complete E-unification
procedure which generalizes Narrowing. This sheds some light on the boundary between
arbitrary E-unification situations and E-unification under canonical E. … Of course we will
expect soundness: an E-unification procedure is sound (for E) if it never returns
substitutions which are not E-unifiers. All of the procedures considered in this paper are …

Let E be a set of equations. An E-uni er of terms A and B is a substitution such that A and B
are equal under E. This paper considers the problem of E-uni cation for arbitrary equational
theories E, and presents an inference rule approximating Paramodulation and leading to a
complete E-uni cation procedure which generalizes Narrowing. This sheds some light on the
boundary between arbitrary E-uni cation situations and E-uni cation under canonical E. We
embrace the point of view that transformations on systems represent a\proof theory" for E-uni …