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I'm interested in properties of relations. Things like completeness (connected, total), transitivity, euclideanness, symmetry and so on. I am interested in the logical connections between these relations. For example, symmetry implies not asymmetry. Or a reflexive, weakly connected relation is complete.

Is there a neat summary of these sorts of properties and their connections?

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    http://en.wikipedia.org/wiki/Relation_algebra, also http://en.wikipedia.org/wiki/Logical_matrix2014-12-09

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Relation between relations, huh? A compilation of properties of relation classes, and then how those properties are related?

Wikipedia on Binary relations has a table near the bottom where you can compare relation classes a little. Mostly these kinds of comparisons are straightforward to prove.

Unexpectedly, an area where these properties are manipulated and interact is in the area of Modal logic, where a given axiom implies a relation among the worlds of a Kripke structure. A number of very minor derivations are of the form "S4 + X = S5, because adding the X axiom adds the symmetric property to a transitive worlds relation which implies that it is an equivalence relation" (modulo actual correct use of those properties!).

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    @Seamus: Sure, but the named classes are often a set of properties you care about, and you care about them because there are so many properties implied by only a few initial properties. That is, instead of taking every possible combination of properties to see which other properties they might imply, it's actually easier to look at the named classes. Rather than looking for a list of the kind you want (which doesn't seem to exist), a good exercise maybe you should try and come up with the list yourself (take pairs of properties and see what they imply). Then compare with the table of classes.2011-03-31
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Is this the kind of summary you are looking for?

http://anglocatholicninjas.wordpress.com/2007/03/20/transitive-symmetric-and-reflexive-relations/

http://en.wikipedia.org/wiki/Equivalence_relation

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    I was looking for something more comprehensive2011-03-31