Retrograde analysis
Retrograde analysis is a genre of chess problem, in which the legality of the position is a key element. A position is legal if it can be reached through a legal chess game (no matter how weird).
Retros (i.e. problems with a Retrograde Analysis content) may ask, for example, for a mate in two, but the main content (at least in modern retros) is in explaining the history of the position. Part of it anyway. This is essentially a matter of logical reasoning, with high appeal for puzzle enthusiasts.
Raymond M. Smullyan wrote two very nice 'Retrograde analysis' riddle books:
