Boole代数的等价刻画

Equivalent characterization of Boolean algebra

目的给出Boole代数的等价刻画,揭示Boole代数和二值命题逻辑的另一种内在联系,使Boole代数更便捷地和其他代数联系。方法从二值逻辑的公理集入手,运用推理,证明,举例的方法进行了讨论。结果得出了Boole代数的等价刻画以及等价刻画中各条公理的独立性.并且利用等价刻画,讨论了Boole代数与其它代数的关系。结论Boole代数新定义的引入为进一步认识和研究Boole代数提供了新的途径。

Aim To discuss equivalent characterization of Boolean algebra and show the relation between Boolean algebra and logic system L and some other algebra systems. Methods Inference, proof, and examples are used to discuss the problem. Results Axioms of equivalent characterization is simplest and which is proved to be , cquivalent to the Boolean algebra. The relationships among Boole- an algebra and some other algebra systems are also discussed. Conclusion This equivalent characterization offers a new way for us to investigate Boolean algebra from a new angle.