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I would be very interested to hear more about the connections between linear logic on the one hand, and probability and game theory (and by extension, GANs) on
by autopoiesis 8y ago
I would be very interested to hear more about the connections between linear logic on the one hand, and probability and game theory (and by extension, GANs) on the other. Could you expand a little on those claims, or provide references?
(Edited for grammatical clarification.)
- adamnemecek 8y agoGAN is based on a minimax algorithm (as mentioned in the paper). Linear logic has very minimaxy semantics.
- autopoiesis 8y agoI was actually more interested in a reference making an explicit construction of a probability theory using linear logic, or if that's unavailable, then some more on the LL -> games -> probability route. Edit: I found this comment [1] by you 29 days ago. Would you mind expanding on the "more connections" you mention? Thanks. [1] https://news.ycombinator.com/item?id=17432612 https://news.ycombinator.com/item?id=17432612
- deleted 8y ago[deleted]
- YorkshireSeason 8y agoWhat is the semantics of Linear Logic?
- adamnemecek 8y agoIt has several interpretations. One is close to game theory, one is related to ownership, one is related to probability, one is related to interfaces. These are all the same idea.
- YorkshireSeason 8y agoAre they for full LL or just small fragments (like MALL)? And what kind of completeness properties are known to hold or not to hold for those models?
- AstralStorm 8y agoYou have normal additive (and/with, or/plus) and multiplicative operators (forall/times, nonsuch/par) as well as exponential ones (ofcourse/ever, whynot/sometimes). The final two are the linear part as they cause the logic to be positional. The closest CS equivalent are categorial grammars (including combinatorial ones), the difference is that pure linear logic is commutative while these are not in general.
- YorkshireSeason 8y agoI'd actually like to see a coherent explanation, e.g. paper reference, of how the Minimax [1] algorithm relates to Girard's linear logic. [1] https://en.wikipedia.org/wiki/Minimax https://en.wikipedia.org/wiki/Minimax
- adamnemecek 8y agoNow we are talking! Check out the paper "Stochastic Interaction and Linear Logic" by Lincoln, Mitchell, Scedrov
- YorkshireSeason 8y agoAs far as I understand, that paper talks only about MALL, which is a small propositional fragment of LL's, in particular, exponentials are missing. Extending models for small fragments to full LL has always been difficult. Note that the Lincoln et al paper is > 2 decades old. Has anyone extended it to full LL? Note also that this paper doesn't seem to be talking about Minimax.