论文标题
Rosser的基本不可证实的定理足以有多少命题逻辑需要多少？
How Much Propositional Logic Suffices for Rosser's Essential Undecidability Theorem?
论文作者
论文摘要
在本文中，我们探讨了以下问题：对于弱算术理论而言，Rosser的基本不可证明的结果可能会造成较弱的逻辑？众所周知，鲁滨逊的Q在直觉逻辑上基本上是不可确定的，而P. Hajek在Grzegorczyk的Q变体的模糊逻辑BL中证明了它，该变体将算术操作解释为非交易的非功能性关系。我们提供了在弱化的下结构逻辑和弱算术理论（Robinson r的版本）中的基本不可证明的证明（算术操作也将其解释为仅仅是关系）。我们的结果是基于克莱恩（Kleene）引入的不可证明参数的结构版本，我们表明它远远超出了布尔，直觉或模糊逻辑的范围。
In this paper we explore the following question: how weak can a logic be for Rosser's essential undecidability result to be provable for a weak arithmetical theory? It is well known that Robinson's Q is essentially undecidable in intuitionistic logic, and P. Hajek proved it in the fuzzy logic BL for Grzegorczyk's variant of Q which interprets the arithmetic operations as non-total non-functional relations. We present a proof of essential undecidability in a much weaker substructural logic and for a much weaker arithmetic theory, a version of Robinson's R (with arithmetic operations also interpreted as mere relations). Our result is based on a structural version of the undecidability argument introduced by Kleene and we show that it goes well beyond the scope of the Boolean, intuitionistic, or fuzzy logic.
