In Cieśliński (J Philos Logic 39:325–337, 2010), Cieśliński asked whether compositional truth theory with the additional axiom that all propositional tautologies are true is conservative over Peano Arithmetic. We provide a partial answer to this question, showing that if we additionally assume that truth predicate agrees with arithmetical truth on quantifier-free sentences, the resulting theory is as strong as \(\Delta _0\)-induction for the compositional truth predicate, hence non-conservative. On the other hand, it can be shown with a routine argument that the principle of quantifier-free correctness is itself conservative.

在 Cieśliński (J Philos Logic 39:325–337, 2010) 中，Cieśliński 询问带有所有命题同义反复都是真的附加公理的组合真理论是否比皮亚诺算术保守。我们对这个问题提供了部分答案，表明如果我们另外假设真值谓词与无量词句子上的算术真值一致，则所得理论与组合真值谓词的 \(\Delta _0\) 归纳一样强大，因此是非保守的。另一方面，可以用常规论证证明，无量词正确性原则本身是保守的。