JUCS - Journal of Universal Computer Science 26(10): 1331-1342, doi: 10.3897/jucs.2020.069
Graphic Deduction Based on Set
Xia He‡, Guoping Du§, Long Hong|‡ Huaiyin Institute of Technology, Huaian, China§ Chinese Academy of Social Sciences, Beijing, China| Nanjing University of Posts and Telecommunications, Nanjing, China
Corresponding author: Xia He ( hxhg@hyit.edu.cn ) © Xia He, Guoping Du, Long Hong. This is an open access article distributed under the terms of the Creative Commons Attribution License (CC BY-ND 4.0). This license allows reusers to copy and distribute the material in any medium or format in unadapted form only, and only so long as attribution is given to the creator. The license allows for commercial use. Citation:
He X, Du G, Hong L (2020) Graphic Deduction Based on Set. JUCS - Journal of Universal Computer Science 26(10): 1331-1342. https://doi.org/10.3897/jucs.2020.069 |  |
Abstract
Based on basic concept of symbolic logic and set theory, this paper focuses on judgments and attempts to provide a new method for the study of logic. It establishes the formal language of the extension of judgment J*, and formally describes a, e, i, o judgment, and thus gives set theory representation and graphical representation that can distinguish between universal judgments and particular judgments. According to the content of non-modal deductive reasoning in formal logic, it gives weakening theorem, strengthening theorem and a number of typical graphical representation theorem (graphic theorem), where graphic deduction is carried out. Graphic deduction will be beneficial to the research of artificial intelligence, which is closely related to judgment and deduction in logic.
Keywords
formal logic, judgement, predicate, graphical representation, graphical theorem, graphical deduction