Partial states are sometimes useful during state space search, especially tree search. Rather than filling in all the featres of a state, some are left undefined and the search progressively fills in values. For example, when trying to complete a Su Doku puzzle, initially the puzzle only has a few numbers filled in and you gradually add additional numbers. Because the state is only part complete, it may not be possible to tell of it is a feasible solution (that is satisfies every constraint) or the full value of a optimisation criterion, but it may be sufficient for a heuristic or to prune some branches.
Used in Chap. 4: page 39
Partially completed magic square with missing values
Search tree for a 3x3 magic square with the partial states being gradually completed at each level.