In universal algebra

Universal algebra

Universal algebra is the field of mathematics that studies algebraic structures themselves, not examples of algebraic structures....

, a quasiidentity is an implication of the form

s₁ = t₁ ∧ … ∧ s_n = t_n → s = t

where s₁, ..., s_n, s and t₁, ..., t_n,t are terms built up from variables using the operation symbols of the specified signature

Signature (logic)

In logic, especially mathematical logic, a signature lists and describes the non-logical symbols of a formal language. In universal algebra, a signature lists the operations that characterize an algebraic structure. In model theory, signatures are used for both purposes.Signatures play the same...

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Quasiidentities amount to conditional equations for which the conditions themselves are equations. A quasiidentity for which n = 0 is an ordinary identity

Identity (mathematics)

In mathematics, the term identity has several different important meanings:*An identity is a relation which is tautologically true. This means that whatever the number or value may be, the answer stays the same. For example, algebraically, this occurs if an equation is satisfied for all values of...

 or equation, whence quasiidentities are a generalization of identities. Quasiidentities are special type of Horn clause

Horn clause

In mathematical logic, a Horn clause is a clause with at most one positive literal. They are named after the logician Alfred Horn, who first pointed out the significance of such clauses in 1951...

s.