#linear logic

[everyfourththing]

Whitehead’s Criteria for Metaphysical Theories

Note that consistency and coherency are considered rational, and that applicability and adequacy are considered empirical. This has importance for Heideggar’s Fourfold since the rational is r…

[processes]

https://en.wikipedia.org/wiki/Linear_logic

"⅋" redirects here Linear logic is a substructural logic proposed by Jean-Yves Girard as a refinement of classical and intuitionistic logic, joining the dualities of the former with many of the constructive properties of the latter.[1] Although the logic has also been studied for its own sake, more broadly, ideas from linear logic have been influential in fields such as programming languages, game semantics, and quantum physics (because linear logic can be seen as the logic of quantum information theory),[2] as well as linguistics,[3] particularly because of its emphasis on resource-boundedness, duality, and interaction.

Linear logic lends itself to many different presentations, explanations and intuitions. Proof-theoretically, it derives from an analysis of classical sequent calculus in which uses of (the structural rules) contraction and weakeningare carefully controlled. Operationally, this means that logical deduction is no longer merely about an ever-expanding collection of persistent "truths", but also a way of manipulating resources that cannot always be duplicated or thrown away at will. In terms of simple denotational models, linear logic may be seen as refining the interpretation of intuitionistic logic by replacing cartesian closed categories by symmetric monoidal categories, or the interpretation of classical logic by replacing boolean algebras by C*-algebras[citation needed].

[maxwithasterisk]

Ever since Jean-Yves Girard discovered linear logic in 1986, researchers around the world have been going “wow! resource tracking, this must be useful for programming languages”. After all, any real computation on a real machine takes resources (memory pages, disk blocks, interrupts, buffers etc) that then aren’t available anymore unless restored somehow. But despite this match apparently made in heaven, research on this subject has remained largely theoretical. It was becoming easy to just give up and assume this nut was simply too tough to crack. We ourselves have been there, but we recovered: we’re having a go at extending GHC with linear types.

[awasim]

via lobste.rs