IMPLICATION ALGEBRA ON A PARTIALLY ORDERED SET AND HEYTING ALGEBRA

摘要

Implication algebra on a partially ordered set is a kind of algebraic abstraction of implicative connection of logic system which value is in a partially ordered set. Heyting algebra is introduced as the algebraic model of intuition proposition logic. In this paper, a implication algebra structure is defined on a partially ordered set, some properties of the Implication Algebra are discussed. And from the view of lattice theory, some relations between this kind of Implication Algebra and Heyting Algebra are given.