试论谓词演算的几何化问题

AN ATTEMPT AT DISCUSSING GEOMETRIZATION PROBLEM OF PREDICATE CALCULUS

本文试图进一步实现G.W.Leibniz提出的数理逻辑几何化设想。为此,探讨了谓词演算的几何建模与图象算法。文中提出了:①量词状态图象及其分析的新理论;②量词对联结词的约束及谓词公式图象算法的独特见解。所举实例表明,这种几何化理论与方法通过作图与符号的结合来进行逻辑运算(推理)及其应用,因而比较直观、简明、快速、方便。

This attempt is to accomplish furtherly the conceiving geometrization of mathematical logicby G.W.Leibniz.For this purpose the construction of geometrical models and the calculation ofthe images on predicate calculus are disscused.This article presents that:①the new theory ofguantifying-state image and its analysis;②the peculiar view of the connective bounded by guan-tifer and the calculation of the images on predicate formulas.These examples prove that:the pre-sented theory and method of geometrization is about how to conduct some logical operations(de-ductions)through the combination of making drawing and symbols,and about how to put theminto practice,so that the operations can go rather intuitively,concisely,rapidly and conveniently.