Such a partial order can also be called consistently or coherently complete (Visser 2004, p. 182), since any upper bound of a set can be interpreted as some consistent (non-contradictory) piece of information that extends all the information present in the set.
This view closely relates to the idea of information ordering that one typically finds in domain theory.
Hence it is important to distinguish between a bounded-complete poset and a bounded complete partial order (cpo).
For a typical example of a bounded-complete poset, consider the set of all finite decimal numbers starting with "0."
Now these elements can be ordered based on the prefix order of words: a decimal number n is below some other number m if there is some string of digits w such that nw = m. For example, 0.2 is below 0.234, since one can obtain the latter by appending the string "34" to 0.2.