I think it would look like a preorder, except that some edges (necessarily between different objects) would be labelled as "maybe" and all paths that include a "maybe" edge should be counted as "maybe", too. For example, if we are dealing with a set of propositions and we interpret edges (or lack thereof) as "there is no proof/there may be a proof/there is a proof", then there would be a proof between two propositions linked by a path of "yes" edges, there may be a proof between two propositions linked only by a path of "yes" and (at least one) "maybe" edges, and there is no proof otherwise (i.e., "no" means "no edges").