Łukasiewicz命题演算形式系统公理独立性证明

A Proof of Independence of Axioms inŁukasiewicz’s Formal System for Propositional Calculus

在有关Łukasiewicz命题演算形式系统的公理独立性证明中,一种常见的做法是直接运用模型论的方法构造出若干三值模型来表明各公理的独立性。不过,这种做法既没有详细解释构造这些三值模型的原因和依据,也没有系统说明构造这些三值模型的过程和方法。实际上,一种直观而自然的思考进路完全可以弥补上述做法的不足。

Among the known proofs of independence of axioms in so-calledŁukasiewicz’s formal system for propositional calculus,a common way is by the model-theoretic method to construct several of three-value models which can present the independence of different axioms.The common way,however,doesn’t adequately investigate the reasons and the grounds by which those three-value models come to happen,and doesn’tsystematically explain the processes and the methods by which those three-value models come to be constructed,either.As a matter of fact,a kind of natural and intuitive thinking approach can completely rule out the defects of the common way.