Logic and Partially Ordered Abelian Groups
Logic
2007-05-23 v1
Abstract
The unit interval in a partially ordered abelian group with order unit forms an interval effect algebra (IEA) which can be regarded as an algebraic model for the semantics of a formal deductive logic. There is a categorical equivalence between the category of IEA's and the category of unigroups enabling one to translate logical features of the IEA's to algebraic properties of the corresponding unigroup. In this article, we study the IEA-unigroup connection, focusing on the cases in which the IEA is a Boolean algebra, a quantum logic, an MV-algebra, or a Heyting MV-algebra.
Keywords
Cite
@article{arxiv.math/0504553,
title = {Logic and Partially Ordered Abelian Groups},
author = {David J. Foulis},
journal= {arXiv preprint arXiv:math/0504553},
year = {2007}
}
Comments
This article is largely expository, although there are some new results concerning Heyting MV-algebras