具有不同替换规则的确定性序列系统的层次结构

IF 0.7 Q4 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

PATTERN RECOGNITION AND IMAGE ANALYSIS Pub Date : 2024-04-10 DOI:10.1134/s1054661824010206

Hakob A. Tamazyan, Anahit A. Chubaryan

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引用次数: 0

摘要

摘要以著名的谢廷变换为基础，介绍了经典命题微积分的确定性序列系统 DS。证明该系统 DS 与命题解析系统 R 和命题无割序列系统 PK- 多项式等价。然后，我们定义了 SDS 系统（具有替换规则的 DS）和 SkDS 系统（具有受限替换规则的 DS，其中替换公式中的连接词数以 k 为界）。我们证明，对于每一个 k≥0 的系统 Sk+1DS 都比树形系统 SkDS 有指数级的速度提升，而且系统 SDS 在多项式上等价于弗雷格系统。

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A Hierarchy of Determinative Sequent Systems with Different Substitution Rules

Abstract

A determinative sequent system DS for the classical propositional calculus is introduced on the base of well-known Tseitin’s transformation. It is proved that the system DS is polynomially equivalent to the propositional resolution system R and propositional cut-free sequent system PK^–. Then we define the system SDS (DS with a substitution rule) and the systems S_kDS (DS with restricted substitution rules, where the number of connectives in substituted formulas is bounded by k). It is proved that for every k ≥ 0 the system S_k+1DS has an exponential speed-up over the system S_kDS in the tree form, and the system SDS is polynomially equivalent to the Frege systems.

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来源期刊

PATTERN RECOGNITION AND IMAGE ANALYSIS Computer Science-Computer Graphics and Computer-Aided Design

CiteScore

1.80

自引率

20.00%

发文量

期刊介绍： The purpose of the journal is to publish high-quality peer-reviewed scientific and technical materials that present the results of fundamental and applied scientific research in the field of image processing, recognition, analysis and understanding, pattern recognition, artificial intelligence, and related fields of theoretical and applied computer science and applied mathematics. The policy of the journal provides for the rapid publication of original scientific articles, analytical reviews, articles of the world''s leading scientists and specialists on the subject of the journal solicited by the editorial board, special thematic issues, proceedings of the world''s leading scientific conferences and seminars, as well as short reports containing new results of fundamental and applied research in the field of mathematical theory and methodology of image analysis, mathematical theory and methodology of image recognition, and mathematical foundations and methodology of artificial intelligence. The journal also publishes articles on the use of the apparatus and methods of the mathematical theory of image analysis and the mathematical theory of image recognition for the development of new information technologies and their supporting software and algorithmic complexes and systems for solving complex and particularly important applied problems. The main scientific areas are the mathematical theory of image analysis and the mathematical theory of pattern recognition. The journal also embraces the problems of analyzing and evaluating poorly formalized, poorly structured, incomplete, contradictory and noisy information, including artificial intelligence, bioinformatics, medical informatics, data mining, big data analysis, machine vision, data representation and modeling, data and knowledge extraction from images, machine learning, forecasting, machine graphics, databases, knowledge bases, medical and technical diagnostics, neural networks, specialized software, specialized computational architectures for information analysis and evaluation, linguistic, psychological, psychophysical, and physiological aspects of image analysis and pattern recognition, applied problems, and related problems. Articles can be submitted either in English or Russian. The English language is preferable. Pattern Recognition and Image Analysis is a hybrid journal that publishes mostly subscription articles that are free of charge for the authors, but also accepts Open Access articles with article processing charges. The journal is one of the top 10 global periodicals on image analysis and pattern recognition and is the only publication on this topic in the Russian Federation, Central and Eastern Europe.