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WHY “SUBLOGIC”? (A STUDY IN UNIVERSAL LOGIC)

机译:为什么“ SUBLOGIC”? (通用逻辑研究)

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In this paper we provide many different reasons to support a fundamental problem “Why sublogic?” for logicains and computer scientists through taking Béziau’s Translation Paradox as the beginning. Historically speaking, we see intuitionistic propositional logic (IPL) firstly as a sublogic of classical propositional logic (CPL). However, it is shown that CPL could be translated into IPL and not on the contrary, i.e., we could find a copy of CPL in IPL (Béziau’s Paradox). It seems that we could not say IPL is indeed weaker or stronger than CPL. We should make the meaning of sublogic and the strength of logics clear in the framework of logical translation. Besides, we intend to promote a new viewpoint of seeing the sub-super relation between logics based on the spirit of universal logic (Section 2). It is helpful for us to provide another nice reason to explain the question, “Why sublogic?”.
机译:在本文中,我们提供许多不同的理由来支持一个基本问题“为什么要使用子逻辑?”以贝索(Béziau)的《翻译悖论》为开端,为逻辑学家和计算机科学家服务。从历史上讲,我们首先将直觉命题逻辑(IPL)视为经典命题逻辑(CPL)的子逻辑。但是,事实证明CPL可以翻译成IPL,而不是相反,也就是说,我们可以在IPL中找到CPL的副本(贝济乌的悖论)。似乎我们不能说IPL确实比CPL弱或强。我们应该在逻辑翻译的框架中明确子逻辑的含义和逻辑的强度。此外,我们打算基于通用逻辑的精神,提倡一种新的观点,即看逻辑之间的次超关系(第二部分)。提供另一个很好的理由来解释问题“为什么选择子逻辑?”对我们很有帮助。

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