Syllogisms in Rudimentary Linear Logic, Diagrammatically
Logic in Computer Science
2013-03-01 v1 Logic
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.
Cite
@article{arxiv.1302.7111,
title = {Syllogisms in Rudimentary Linear Logic, Diagrammatically},
author = {Ruggero Pagnan},
journal= {arXiv preprint arXiv:1302.7111},
year = {2013}
}