Graphic Deduction Based on Set

Xia He (Huaiyin Institute of Technology, China)

Guoping Du (Chinese Academy of Social Sciences, China)

Long Hong (Nanjing University of Posts and Telecommunications, China)

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, graphical deduction, graphical representation, graphical theorem, judgement, predicate

Categories: F.4, I.2.4, I.3.6