The notion of cylindric algebra, invented by Alfred Tarski, arises naturally in the algebraization of first-order logic. This is comparable to the role Boolean algebras play for propositional logic. Indeed, cylindric algebras are Boolean algebras equipped with additional cylindrification operations that model quantification. // Alfred Tarski (January 14, 1902, Warsaw, Russian-ruled Poland – October 26, 1983, Berkeley, California) was a logician and mathematician who spent four decades as a professor of mathematics at the University of California, Berkeley. ... Algebraic logic has at least two meanings: the early study of Boolean algebra; and abstract algebraic logic, a branch of contemporary mathematical logic. ... First-order logic (FOL) is a universal language in symbolic science, and is in use everyday by mathematicians, philosophers, linguists, computer scientists and practitioners of artificial intelligence. ... In abstract algebra, a Boolean algebra is an algebraic structure (a collection of elements and operations on them obeying defining axioms) that captures essential properties of both set operations and logic operations. ... Propositional logic or sentential logic is the logic of propositions, sentences, or clauses. ... In language and logic, quantification is a construct that specifies the extent of validity of a predicate, that is the extent to which a predicate holds over a range of things. ...

Recently, cylindric algebras have been generalized to the many-sorted case, which allows for a better modeling of the duality between first-order formulas and terms.

See also

• Abstract algebraic logic

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References

• Henkin, L. and Monk, J.D. and Tarski, A. (1971) Cylindric Algebras, Part I. North-Holland. ISBN 978-0-7204-2043-2.
• C. Caleiro and R. Gonçalves. On the algebraization of many-sorted logics. Preprint, SQIG - IT and IST, 1049-001 Lisboa, Portugal, 2006. Submitted for publication.