Syllogisms in Rudimentary Linear Logic, Diagrammatically

Ruggero Pagnan

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arXiv · 1302.7111

Syllogisms in Rudimentary Linear Logic, Diagrammatically

Ruggero Pagnan

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Abstract

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.

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Ruggero Pagnan. 2013-02-28. Syllogisms in Rudimentary Linear Logic, Diagrammatically. https://arxiv.org/abs/1302.7111

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