Logic and Partially Ordered Abelian Groups
نویسنده
چکیده
The unit interval in a partially ordered abelian group with order unit forms an interval effect algebra (IEA) and 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. In this article, we study the IEA-unigroup connection, focusing on the cases in which the IEA is a Boolean algebra, an MV-algebra, a Heyting MV-algebra, or a quantum logic. AMS Classification: Primary 03G10. Secondary 06F20.
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