所有可证明谓词的可证明性逻辑

IF 0.7 4区数学 Q3 COMPUTER SCIENCE, THEORY & METHODS

Journal of Logic and Computation Pub Date : 2023-09-25 DOI:10.1093/logcom/exad060

Taishi Kurahashi

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引用次数: 0

摘要

摘要证明了所有可证明谓词的可证明性逻辑是完全拟合的、Marek的和Truszczyński的纯必然性逻辑$\textsf{N}$。此外，我们还引入了$\textsf{N}$的三个扩展$\textsf{N4}$, $\textsf{NR}$和$\textsf{NR4}$，并研究了这些逻辑的算术语义。事实上，我们证明了$\textsf{N4}$、$\textsf{NR}$和$\textsf{NR4}$分别是满足可导性条件的第三个条件$\textbf{D3}$的所有可证明性谓词、所有Rosser可证明性谓词和所有Rosser可证明性谓词满足$\textbf{D3}$的所有可证明性逻辑。

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The provability logic of all provability predicates

Abstract We prove that the provability logic of all provability predicates is exactly Fitting, Marek, and Truszczyński’s pure logic of necessitation $\textsf{N}$. Moreover, we introduce three extensions $\textsf{N4}$, $\textsf{NR}$ and $\textsf{NR4}$ of $\textsf{N}$ and investigate the arithmetical semantics of these logics. In fact, we prove that $\textsf{N4}$, $\textsf{NR}$ and $\textsf{NR4}$ are the provability logics of all provability predicates satisfying the third condition $\textbf{D3}$ of the derivability conditions, all Rosser provability predicates and all Rosser provability predicates satisfying $\textbf{D3}$, respectively.

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来源期刊

Journal of Logic and Computation 工程技术-计算机：理论方法

CiteScore

1.90

自引率

14.30%

发文量

审稿时长

6-12 weeks

期刊介绍： Logic has found application in virtually all aspects of Information Technology, from software engineering and hardware to programming and artificial intelligence. Indeed, logic, artificial intelligence and theoretical computing are influencing each other to the extent that a new interdisciplinary area of Logic and Computation is emerging. The Journal of Logic and Computation aims to promote the growth of logic and computing, including, among others, the following areas of interest: Logical Systems, such as classical and non-classical logic, constructive logic, categorical logic, modal logic, type theory, feasible maths.... Logical issues in logic programming, knowledge-based systems and automated reasoning; logical issues in knowledge representation, such as non-monotonic reasoning and systems of knowledge and belief; logics and semantics of programming; specification and verification of programs and systems; applications of logic in hardware and VLSI, natural language, concurrent computation, planning, and databases. The bulk of the content is technical scientific papers, although letters, reviews, and discussions, as well as relevant conference reviews, are included.