Quasi-identity

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 amount to a conditional equation for which the conditions themselves are equations. Alternatively, it can be seen as a disjunction of equations s₁ = t₁ ∨ ... ∨ s_n = t_n ∨ s = t. A quasi-identity for which n = 0 is an ordinary identity or equation, whence quasi-identities are a generalization of identities. Quasi-identities are special type of Horn clauses.

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.