> Non-Boolean logics are rare, and relations more general than partial order are almost never useful. That's a bold claim! In set theory, a relation is just so

> Non-Boolean logics are rare, and relations more general than partial order are almost never useful. That's a bold claim! In set theory, a relation is just some set of pairs made from some base set of elements. I guess the sentence should say "orderings more exotic than the partial order" instead or something, to be more specific. For example, if I'm implementing a Sokoban engine, I might define a "step" relation on game states, informally saying that two game states are "step"-related if you can get from one state to the other in a single move. From another perspective, this is just an implicit definition of the edges in a large or infinite graph of game states. That's because the concept of a set-theoretic relation is in a sense isomorphic to the concept of a graph-theoretic edge set: A relation is a subset of the possible pairs of elements, just like an edge set is a subset of the possible pairs of vertices. And just like a relation can be symmetric ("for all a,b, if a is related to b, then b is related to a"), so can an edge set be symmetric or undirected.