[msp-interest] [MSP101] Ross Horne: Additives without Weakening (LT412, 3pm Mon 17-Mar)

[Dilsat Yuksel]

Hi,

On Monday, the MSP101 talk will be given by Ross Horne (MSP, StrathCyber). See the details of the talk below.

Best,
Dilsat

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Date: Monday, 17 March at 15:00

Room: LT412, Livingstone Tower

Zoom link: https://strath.zoom.us/j/85449272187?pwd=0qNkQqybiaKgBpbEBRv38x11x4db5n.1
Live stream on Youtube: https://www.youtube.com/@msp101strathclyde4

Speaker: Ross Horne

Title: Additives without Weakening

Abstract: As we know, in linear logic, conjunction and disjunction decompose into separate multiplicative and additive forms. Only additives are idempotent in general (A + A --o A). The additives also have some properties such as weakening (A & B --o A). By dropping weakening, the additives further decompose into infinitely many sub-additive operators.
I explain how I spotted these sub-additive operators when studying nominal quantifiers that can similarly be decomposed into new nominal quantifiers. I found these new additives curious since the resulting operators have properties that are sound with respect to probability distributions, effectively internalising probability distributions in logic. I end by giving a taste of the proof theory of the sub-additives. A novelty is that, due to how sub-additives control certain distributivity properties that play an essential role in established cut elimination techniques, a new proof technique must be invented.

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