Quasi-identity
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Revision as of 13:45, 31 July 2022 by imported>Ohm (linkage)
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 ∧ … ∧ sn = tn → s = t
where s1, ..., sn, t1, ..., tn, 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 ∨ ... ∨ sn ≠ tn ∨ 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
References
- Burris, Stanley N.; H.P. Sankappanavar (1981). A Course in Universal Algebra. Springer. ISBN 3-540-90578-2. Free online edition.
![]() | Original source: https://en.wikipedia.org/wiki/Quasi-identity.
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