What is "quasiidentity"

n. (context mathematics English) A kind of Horn clause, a generalization of identity.

In universal algebra, a quasiidentity is an implication of the form

where s, ..., s, s and t, ..., t,t are terms built up from variables using the operation symbols of the specified signature.

Quasiidentities amount to conditional equations for which the conditions themselves are equations. A quasiidentity for which n = 0 is an ordinary identity or equation, whence quasiidentities are a generalization of identities. Quasiidentities are special type of Horn clauses.