Talk:Brazilian logic

This page can't be right. I don't think Brazilian logic refers to a relevant logic at all. But if it does, then the statement about dualities and open/closed sets looks wrong. (Or maybe I'm applying non-Brazilian logic to the situation, and I should just accept the contradiction.) -Dan 19:43, 21 November 2005 (UTC)

My understanding of what was written was that it meant that the logic can be specified by a sequent calculus where there are only structural rules on the right, as opposed to only on the left as in LJ. The claim doesn't strike me as implausible, but it would be good if we could check this claim, anyway. --- Charles Stewart 20:17, 21 November 2005 (UTC)[reply]

Sure, the duality part is plausible on its own, but the article as a whole is not. For instance, without left-structural rules, the law of non-contradiction is not derivable (is it?) contrary to what the article says. -Dan 16:06, 23 November 2005 (UTC)

Also weakening would still be available, which defeats the point of relevant logic. -Dan 16:11, 23 November 2005 (UTC)

I wonder how the rule of non-contradiction is derived, but I'm not confident enough of my graspo of this unfamiliar calculus to say it can't be done. The classical paradoxes of material implication concern left weakening: I can imagine arguing that a calculus with right but not left weakening is relevant. I'd like to see sources for all of this, but it doesn't strike me as implausible. --- Charles Stewart 19:36, 23 November 2005 (UTC)[reply]

Alright, so I did a bit of web searching. It's hard to track down "Brazilian logic". But this page looks like it was copied and pasted from [1] with some editing -- but there, R# and "Brazilian logic" are different systems. Also it says the law of non-contradiction does not hold in "Brazilian logic". -Dan 21:01, 25 November 2005 (UTC)

I've redirected this page to Paraconsistent logic. "Brazilian logic" seems to be a term used only by Mortensen (and perhaps a few others) for a particular variety of paraconsistent logic. It doesn't seem to merit its own article. Since the current content of the article seems to be incorrect (see above), I'm not merging it into Paraconsistent logic. If anyone wants to add something interesting and verifiable about "Brazilian logic" to the Paraconsistent logic article, he or she is welcome and encouraged to do so. dbtfz^talk 02:38, 26 February 2006 (UTC)[reply]

I undid the redirect, since a few articles link specifically to Brazilian logic. I'm not sure what to do with this, esp. since I'm not too familiar with Mortensen's work--specifically, what he means by "Brazilian logic." I think he might just mean Newton da Costa's approach to paraconsistent logic (with which I am reasonably familiar), but I'm not sure. Perhaps this topic should be covered in Paraconsistent logic and/or Newton da Costa instead of having an article of its own... dbtfz^talk 03:41, 26 February 2006 (UTC)[reply]

OK, here's what I propose to do (when I or someone else gets around to it): redirect the article to Paraconsistent logic, and add a brief section to Paraconsistent logic that covers this type of logic (a better and more standard name for which is dual-intuitionistic logic—see e.g. [2]). If anyone objects, please speak up now. dbtfz^talk 23:04, 2 March 2006 (UTC)[reply]