广义可实现性与直觉逻辑

IF 0.7 4区数学 Q3 COMPUTER SCIENCE, THEORY & METHODS ACM Transactions on Computational Logic Pub Date : 2022-05-17 DOI:10.1145/3565367

A. Y. Konovalov

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引用次数: 1

摘要

设V是一组数论函数。我们为谓词公式定义了V可实现性的概念，使得V中函数的索引用于解释蕴涵和通用量词。在本文中，我们证明了直觉谓词演算关于V可实现性的语义是健全的，当且仅当V的一些自然条件成立。

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A Generalized Realizability and Intuitionistic Logic

Let V be a set of number-theoretical functions. We define a notion of V-realizability for predicate formulas in such a way that the indices of functions in V are used for interpreting the implication and the universal quantifier. In this article, we prove that Intuitionistic Predicate Calculus is sound with respect to the semantics of V-realizability if and only if some natural conditions for V hold.

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来源期刊

ACM Transactions on Computational Logic 工程技术-计算机：理论方法

CiteScore

2.30

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： TOCL welcomes submissions related to all aspects of logic as it pertains to topics in computer science. This area has a great tradition in computer science. Several researchers who earned the ACM Turing award have also contributed to this field, namely Edgar Codd (relational database systems), Stephen Cook (complexity of logical theories), Edsger W. Dijkstra, Robert W. Floyd, Tony Hoare, Amir Pnueli, Dana Scott, Edmond M. Clarke, Allen E. Emerson, and Joseph Sifakis (program logics, program derivation and verification, programming languages semantics), Robin Milner (interactive theorem proving, concurrency calculi, and functional programming), and John McCarthy (functional programming and logics in AI). Logic continues to play an important role in computer science and has permeated several of its areas, including artificial intelligence, computational complexity, database systems, and programming languages. The Editorial Board of this journal seeks and hopes to attract high-quality submissions in all the above-mentioned areas of computational logic so that TOCL becomes the standard reference in the field. Both theoretical and applied papers are sought. Submissions showing novel use of logic in computer science are especially welcome.

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