可分析集合、笛卡尔逻辑和命题的可推导性关系  

Analytical sets,Cartesian logic and dialectical relations on propositions

作　　者：赵峰 

机构地区：[1]山西焦煤汾西矿业集团

出　　处：《软件》2012年第1期12-22,共11页Software

摘　　要：本文在ZFC公理系统的基础上,首先提出可分析集合的概念且可表达为p={x|x∈p}。然后给出受囿变量的定义,引入笛卡尔逻辑以使逻辑的概念像算法的概念一样精确化而成为明确的数学对象,不仅足以适应代数和分析的要求,而且充分满足经典和非经典逻辑的需要,并探讨命题间的可推导性关系,包括:对立、排中、重言、归谬、反对、矛盾、存在、全称、独立、同一和不矛盾。进而,讨论一些逻辑运算和有关的逻辑问题,并进一步阐述可分析集合的几个基本关系和基本运算。In this paper, first the analytical set is obtained and can be written as p={xix Ep} on the basis of ZF （and ZFC）. Then the bounded variable is presented and Cartesian logic is introduced so that logic could become a distinct mathematical object not only to satisfy fully the requirements of both classical logic and non-classical logic but also to suit sufficiently the needs of both algebra and analysis. Moreover, dialectical relations on propositions are discussed, including the following： opposite; excluded middle; tautology; reduction to absurdity; antithesis; contradiction; existence; universality; independence; identity and non-contradiction. Further, logical operations and some relevant lopical problems are studied. Several of fimdamental relations and operations of analytical sets are also showed in it.

关 键 词：计算机软件 公理集合论 可分析集合 变量 受囿变量 笛卡尔逻辑 命题的可推导性关系 逻辑运算. 

分 类 号：TP3-05[自动化与计算机技术—计算机科学与技术] O14[理学—数学]