论文标题
所有可预辩性谓词的可预行性逻辑
The provability logic of all provability predicates
论文作者
论文摘要
我们证明，所有Provability Predicates的可预行性逻辑完全合适，Marek和Truszczyński的纯粹逻辑$ \ Mathsf {n} $。此外，我们介绍了三个扩展名$ \ MATHSF {N4} $，$ \ MATHSF {NR} $，以及$ \ Mathsf {n} $的$ \ Mathsf {nr4} $，并研究这些逻辑的算术语义。实际上，我们证明$ \ MATHSF {N4} $，$ \ MATHSF {NR} $和$ \ Mathsf {NR4} $是满足第三条件条件$ \ Mathbf {D3} $衍生能力的第三条件$ \ Mathbf {D3} $的所有可证明性的可普及性逻辑，所有这些都可以满足所有范围的预期，并且是All All provications and provicaties and precicaties and precicaties and crosersienty and crosersies and croseriaties and crosersientians and crosery的概述。 $ \ mathbf {d3} $。
We prove that the provability logic of all provability predicates is exactly Fitting, Marek, and Truszczyński's pure logic of necessitation $\mathsf{N}$. Moreover, we introduce three extensions $\mathsf{N4}$, $\mathsf{NR}$, and $\mathsf{NR4}$ of $\mathsf{N}$ and investigate the arithmetical semantics of these logics. In fact, we prove that $\mathsf{N4}$, $\mathsf{NR}$, and $\mathsf{NR4}$ are the provability logics of all provability predicates satisfying the third condition $\mathbf{D3}$ of the derivabiity conditions, all Rosser's provability predicates, and all Rosser's provability predicates satisfying $\mathbf{D3}$, respectively.
