Wednesday, September 03, 2008

Two questions

I thought I'd post a couple of questions, which I'm sort of looking into, while more substantive posts are still in development.

First question: Are there discussions of linear logic anywhere in the philosophical literature? There's a lot on relevance logic and a lot on intuitionistic logic. I'm not sure where to find stuff on linear logic. Failing that, are there any computer science articles that include philosophical discussions of it that go beyond "premises are like resources"? (That's just something I've seen a lot. It is a helpful though opaque metaphor.) I don't know that I have it in me to work through Girard's stuff yet.

Second question: Are there any philosophical books or articles that talk about formal language theory? (I mean more than just Turing machines.) Brandom's Locke lectures have a short discussion of it, mainly the Chomsky hierarchy, early on, but that falls by the wayside and is laden heavily with Brandom's project. I bet there's something neat of a philosophical bent somewhere in the computer science literature, but I have no clue.


Ole Thomassen Hjortland said...

One of the few (non-Girard) attempts I've seen at putting linear logic in a philosophical context is below:

Jacques Dubucs and Mathieu Marion, "Radical Anti-Realism and Substructural Logics", in RojszczakPhilosophicalDimensionsLogicScience, pp. 235-249 (2003)

Francesco Paoli is another author who does some stuff on linear conditionals.

Shawn said...

I suppose I should mention the two-part introduction to linear logic that is available on arxiv. It is called "Introduction to Linear Logic and Ludics" and it is by Pierre-Louis Curien. It is easier going than Girard's stuff.

I have Paoli's book checked out and I've been meaning to look at it. He also talks about hypersequents which I'm curious about.

Thanks for the citations.