Unification involves the search for substitutions that make two terms ""equal"". In syntactic unification, the substitution should make the terms identical; in semantic unification, they should be made equal with respect to some equational theory (e.g., equal in all groups or semigroups). This latter task amounts to solving equations in free algebras of the given theory. On the other hand, solving quasi-equations in these free algebras corresponds to
the problem of determining the admissibility of rules for particular logics or
classes of algebras.
This talk will first introduce some of the core ideas and achievements
of research into semantic unification and then explain their relevance for
characterizing and exploiting admissible rules.

[Invited by L. Ciobanu]