Quasi-identity

Short description: A kind of Horn clause, a generalization of identities

In universal algebra, a quasi-identity is an implication of the form

s₁ = t₁ ∧ … ∧ s_n = t_n → s = t

where s₁, ..., s_n, t₁, ..., t_n, 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 s₁ ≠ t₁ ∨ ... ∨ s_n ≠ t_n ∨ s = t—that 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.

See also

• Quasivariety

References

• Burris, Stanley N.; H.P. Sankappanavar (1981). A Course in Universal Algebra. Springer. ISBN 3-540-90578-2.  Free online edition.