Talk:Relation algebra

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Apparently, this article uses unconventional notation, and it certainly seems crazy to me. Why not use the conventional notation? -Chinju 05:31, 28 March 2007 (UTC)

I second the motion. If we have to use parenthesis to represent boolean negation as in -x=(x), how do we use parenthesis normally in an equation? I suppose that we could express the associative law of addition (union) as ((x+y))+z=x+((y+z)) on the theory that the double parenthesis represents a double negation. As long as we double up on all of our parenthesis, we ought to be safe. ;o) --Ramsey2006 02:38, 29 March 2007 (UTC)

I third it. Relation algebra is just another variety like groups and Boolean algebras, in fact a relation algebra is almost both (it would be exactly both if converse canceled composition). It has no more need of pedantic language-metalanguage distinctions and multiple fonts than group theory or Boolean algebra. I suspect the metalanguage stuff is inherited from the Tarski-Givant book, where they use it to refound various logical formulations of set theory on RA including Zermelo-Fränkel set theory, Von Neumann-Bernays-Gödel set theory, Morse-Kelley set theory, and Vopěnka and Hájek's semisets, a wildly ambitious project well outside the scope of the present article. I propose to replace the first two sections (definition and axioms) with the definition that a relation algebra is a residuated Boolean algebra with converse (the definition given at the end of the examples section of the residuated lattice article), and use the freed-up space to motivate the subject by moving the historical remarks (currently at the end) up to the front and reorganizing them to show what the subject looked like originally and how each of De Morgan (1858), Peirce (1870s), Schröder (1895), and Tarski (1940s) added to and abstracted from the subject. The only decent section in the current article is the one on expressive power, which is very much to the point (who wrote that?). The section on "Other notations" should be reduced to a couple of lines simply listing them. The merits of splitting the RA article into RA (logic) and RA (structure) paralleling the recent BA split are pointed up by the Examples section, which would go in the logic article, while a separate (glaringly omitted) section on examples of relation algebras would go in the RA (structure) article (but such a split should not be needed as long as the reworked article remains reasonably short). Comments? I suggest waiting a week for input before actually implementing any of this. --Vaughan Pratt 22:17, 26 July 2007 (UTC)

The promised rewrite is now pretty much completed (at least I'll be taking a rest from it for a while). In the end I split the material between three articles, on residuated lattices, residuated Boolean algebras, and relation algebras, each adding a little to its predecessor. This enabled relation algebras to be defined as simply residuated Boolean algebras for which ▷I and I◁ are involutions, following Jónsson and Tsinakis. --Vaughan Pratt 06:19, 16 August 2007 (UTC)

[edit] Questionable Statements

Several statements on this page are obviously false. The converse operator isn't an interior operator, since it isn't idempotent (but rather an involution). Also, I'm pretty sure that two non-identity functions can commute with eachother: e.g. f(x) = 2x and g(x) = 3x —The preceding unsigned comment was added by 131.107.0.73 (talk • contribs) 14:54, 20 July 2007.

[edit] Removed strange links

The article seemed to assert (by citation) that the notions of injectivity, surjectivity were invented in 2002. These notions are indeed mentioned briefly in the referenced article, but they were well-known for years before then. I have removed these citations. I've left a (partial) reference to that article at the end of the page. I'm not sure that it is an important general reference, but I leave it to others to decide whether to delete it.

If I have missed an important point, I'm sorry. I'm happy to discuss. Sam Staton 09:35, 27 September 2007 (UTC)