In universal algebra, a quasi-identity is an implication of the form
where s<sub>1</sub>, ..., s<sub>n</sub>, t<sub>1</sub>, ..., t<sub>n</sub>, s, and t are terms built up from variables using the operation symbols of the specified signature.
A quasi-identity amounts to a conditional equation for which the conditions themselves are equations. Alternatively, it can be seen as a disjunction of inequations and one equation s<sub>1</sub> â t<sub>1</sub> ⨠... ⨠s<sub>n</sub> â t<sub>n</sub> ⨠s = tâÂÂthat is, as a definite Horn clause. A quasi-identity with n = 0 is an ordinary identity or equation, so quasi-identities are a generalization of identities.