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Mathematical system of potential infinities (II) – formal systems of logical basis

Wujia Zhu (Department of Computer Science, Nanjing University of Aeronautics and Astronautics, Nanjing, People's Republic of China)
Yi Lin (School of Economics and Management, Nanjing University of Aeronautics and Astronautics, Nanjing, People's Republic of China Department of Mathematics, Slippery Rock University, Slippery Rock, Pennsylvania, USA)
Guoping Du (Institute of Modern Logic and Applications, Nanjing University, Nanjing, People's Republic of China)
Ningsheng Gong (College of Information Science, Nanjing University of Technology, Nanjing, People's Republic of China)

Kybernetes

ISSN: 0368-492X

Article publication date: 11 April 2008

Abstract

Purpose

This is the second part of the effort to resolve the following two problems that badly need an answer: how can an appropriate theoretical foundation be chosen for modern mathematics and computer science? And, under what interpretations can modern mathematics and the theory of computer science be kept as completely as possible?

Design/methodology/approach

The paper sets out the foundation for the system.

Findings

Here, the logical foundation for the mathematical system of potential infinities is given.

Originality/value

The logical calculus, which will be used as the tool of deduction in the PIMS, is established. This new tool of reasoning is a modification of the classical two‐value logical calculus system.

Keywords

Citation

Zhu, W., Lin, Y., Du, G. and Gong, N. (2008), "Mathematical system of potential infinities (II) – formal systems of logical basis", Kybernetes, Vol. 37 No. 3/4, pp. 494-504. https://doi.org/10.1108/03684920810863480

Publisher

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Emerald Group Publishing Limited

Copyright © 2008, Emerald Group Publishing Limited