Cylindric algebra
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.
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
- Lambda calculus and Combinatory logic, other approaches to modelling quantification and eliminating variables
- Hyperdoctrines are a categorical formulation of cylindric algebras
- First-order logic
References
- Leon Henkin, Monk, J.D., and Alfred Tarski (1971) Cylindric Algebras, Part I. North-Holland. ISBN 978-0-7204-2043-2.
- -------- (1985) Cylindric Algebras, Part II. North-Holland.
- Caleiro, C., and Gonçalves, R (2007) "On the algebraization of many-sorted logics" in J. Fiadeiro and P.-Y. Schobbens, eds., Recent Trends in Algebraic Development Techniques - Selected Papers, Vol. 4409 of Lecture Notes in Computer Science. Springer-Verlag: 21-36.
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