TITLE: Logical relations between relations
QUESTION [5 upvotes]: 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?

REPLY [2 votes]: 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!).