In many real-life applications, we have an ordered set: a set of all space-time events, a set of all alternatives, a set of all degrees of confidence. In practice, we usually only have a partial information about an element x of this set. This partial information includes positive knowledge: that a <= x or x <= a for some known a, and negative knowledge: that it is not true that a <= x or x <= a for some known a. In the case of a total order, the set of all elements satisfying this partial information is an interval. We show that in the general case of a partial order, the corresponding analogue of an interval is a convex set. We also show that in general, to describe partial knowledge, it is sufficient to have only negative information about x but it is not sufficient to have only positive information.