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Aristotelian Logic Axioms in Propositional Logic: The Pouch Method
History and Philosophy of Logic ( IF 0.5 ) Pub Date : 2018-04-11 , DOI: 10.1080/01445340.2018.1442172 Enrique Alvarez-Fontecilla 1 , Tomas Lungenstrass 2
History and Philosophy of Logic ( IF 0.5 ) Pub Date : 2018-04-11 , DOI: 10.1080/01445340.2018.1442172 Enrique Alvarez-Fontecilla 1 , Tomas Lungenstrass 2
Affiliation
A new theoretical approach to Aristotelian Logic (AL) based on three axioms has been recently introduced. This formalization of the theory allowed for the unification of its uncommunicated traditional branches, thus restoring the theoretical unity of AL. In this brief paper, the applicability of the three AL axioms to Propositional Logic (PL) is explored. First, it is shown how the AL axioms can be applied to some simple PL arguments in a straightforward manner. Second, the development of a proof method for PL inspired by the AL axioms is presented. This method mimics the underlying mechanics of the proof method from AL, and offers a complementary alternative to proof methods such as truth trees.
中文翻译:
命题逻辑中的亚里士多德逻辑公理:袋法
最近引入了一种基于三个公理的亚里士多德逻辑 (AL) 的新理论方法。理论的这种形式化允许统一其未交流的传统分支,从而恢复 AL 的理论统一性。在这篇简短的论文中,探讨了三个 AL 公理对命题逻辑 (PL) 的适用性。首先,展示了如何以直接的方式将 AL 公理应用于一些简单的 PL 参数。其次,介绍了受 AL 公理启发的 PL 证明方法的发展。这种方法模仿了 AL 证明方法的基本机制,并提供了对证明方法(如真值树)的补充替代方案。
更新日期:2018-04-11
中文翻译:
命题逻辑中的亚里士多德逻辑公理:袋法
最近引入了一种基于三个公理的亚里士多德逻辑 (AL) 的新理论方法。理论的这种形式化允许统一其未交流的传统分支,从而恢复 AL 的理论统一性。在这篇简短的论文中,探讨了三个 AL 公理对命题逻辑 (PL) 的适用性。首先,展示了如何以直接的方式将 AL 公理应用于一些简单的 PL 参数。其次,介绍了受 AL 公理启发的 PL 证明方法的发展。这种方法模仿了 AL 证明方法的基本机制,并提供了对证明方法(如真值树)的补充替代方案。