广义抽象协调类和广义合一原理(英文)

Universal Abstract Consistency Class and Universal Unifying Principle

协调性是数理逻辑中最基本的语法概念之一。Ｓｍｕｌｙａｎ提出了抽象协调类概念，并证明了相应的Ｓｍｕｌｙａｎ合一原理。通过考察协调合式公式集类所具有的种种性质，本文将抽象协调类概念推广至最一般的形式——广义抽象协调类，并证明了相应的广义合一原理。这一结果可以用于证明一阶逻辑形式系统和我们所提出的广义反驳方法的完备性。

Consistency is one of the most fundamental syntactic concepts in mathematical logic. By treating consistency in an abstract way, Smullyan presented abstract consistency class, and proved the socalled Smullyan′s unifying principle. In this paper, considering various properties possessed by the class of consistent sets of wffs in first order logic system, we generalize the concept of abstract consistency class into the most general form-universal abstract consistency class, and further prove its universal unifying principle. This result can be used to prove the completeness theorems of first order logic system and the universal refutation method proposed by us.