Clone Theory and Algebraic Logic
Logic in Computer Science
2009-07-28 v1
Abstract
The concept of a clone is central to many branches of mathematics, such as universal algebra, algebraic logic, and lambda calculus. Abstractly a clone is a category with two objects such that one is a countably infinite power of the other. Left and right algebras over a clone are covariant and contravariant functors from the category to that of sets respectively. In this paper we show that first-order logic can be studied effectively using the notions of right and left algebras over a clone. It is easy to translate the classical treatment of logic into our setting and prove all the fundamental theorems of first-order theory algebraically.
Cite
@article{arxiv.0907.4531,
title = {Clone Theory and Algebraic Logic},
author = {Zhaohua Luo},
journal= {arXiv preprint arXiv:0907.4531},
year = {2009}
}