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Last talk of the Online Seminar Series 2020 — V. M. Abrusci: Syllogism and linear logic

The last talk for the year within the cycle of online seminars organized by the Milan Logic Group will be given by Vito Michele Abrusci on December 3rd, 2020, at 10:30 via Zoom. Please contact us for details for joining and stay tuned to this website for upcoming news on events for 2021.

Abstract.

Discoveries on syllogisms, induced by linear logic, will be presented:

a)     Categorical Propositions and Syllogisms are closed under duality. The system of Aristotelian syllogisms (1st, 2nd and 3rdfigures) is complete under duality. 

b)    Categorical Propositions and Syllogisms may be represented inside multiplicative fragment of Linear Logic (no need of contraction and weakening rules, no need of first order quantifiers). Better understanding of the Aristotelian notion of “contradictory propositions”. 

c)     Syllogisms as proof-nets, and thus as geometrical objects and as programs. 

d)    Why 1st figure syllogisms are simple syllogisms, and the other syllogisms are not simple? A geometrical answer: 1st figure syllogisms are planar proof-nets, whereas other syllogisms are not planar proof-nets. 

e)    Reductions of syllogisms to 1st figure syllogisms are geometrical ways to transform non-planar graphs into planar graphs. 

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