从模态视角看建构主义理论

IF 0.6 4区数学 Q2 LOGIC

Logic Journal of the IGPL Pub Date : 2023-12-30 DOI:10.1093/jigpal/jzad029

Matteo Tesi

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引用次数: 0

摘要

我们提出了一类一阶直观论的哥德尔-麦金赛-塔尔斯基嵌入的统一证明论证。这是通过将证明分析的方法调整到模态逻辑的情况中来实现的，以便将公理转换成合适的序列微积分的推理规则。嵌入的健全性和忠实性是通过对增强计算中导数高度的归纳来证明的。最后，我们定义了一个模态系统的扩展，其结果在几何直观方面是成立的。

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Constructive theories through a modal lens

We present a uniform proof-theoretic proof of the Gödel–McKinsey–Tarski embedding for a class of first-order intuitionistic theories. This is achieved by adapting to the case of modal logic the methods of proof analysis in order to convert axioms into rules of inference of a suitable sequent calculus. The soundness and the faithfulness of the embedding are proved by induction on the height of the derivations in the augmented calculi. Finally, we define an extension of the modal system for which the result holds with respect to geometric intuitionistic.

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来源期刊

Logic Journal of the IGPL 数学-数学

CiteScore

2.60

自引率

10.00%

发文量

审稿时长

6-12 weeks

期刊介绍： Logic Journal of the IGPL publishes papers in all areas of pure and applied logic, including pure logical systems, proof theory, model theory, recursion theory, type theory, nonclassical logics, nonmonotonic logic, numerical and uncertainty reasoning, logic and AI, foundations of logic programming, logic and computation, logic and language, and logic engineering. Logic Journal of the IGPL is published under licence from Professor Dov Gabbay as owner of the journal.