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Syllogisms in Rudimentary Linear Logic, Diagrammatically

机译:基本线性逻辑中的三段论

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摘要

We present a reading of the traditional syllogistics in a fragment of the propositional intuitionistic multiplicative linear logic and prove that with respect to a diagrammatic logical calculus that we introduced in a previous paper, a syllogism is provable in such a fragment if and only if it is diagrammatically provable. We extend this result to syllogistics with complemented terms a la De Morgan, with respect to a suitable extension of the diagrammatic reasoning system for the traditional case and a corresponding reading of such De Morgan style syllogistics in the previously referred to fragment of linear logic.
机译:我们在命题直觉乘法线性逻辑的一个片段中介绍了传统的三段论,并证明对于我们在前一篇论文中介绍的图解逻辑演算,三段论在这种片段中是可证明的,当且仅当它是图表上可证明的。关于对传统案例的图解推理系统的适当扩展,以及在以前提到的线性逻辑片段中对此类De Morgan风格三段论的相应阅读,我们将这一结果扩展到三段论,并使用补充术语la De Morgan。

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