2025-03-17: Ross Horne (MSP)

Thu, 13 Mar 2025 16:23:15 +0000

Ross Horne (MSP)

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.

2025-03-17 15:00:00 UTC
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