Broken is related to Damage. Damage is the opposite of Repair. Piece is a type of Repair. Piece is related to Chunk. 
you are likely to find Pie in/at/on Oven. you are likely to find Cake in/at/on Oven. Cake is related to Item. Item is related to Board. 
Broken <--RelatedTo--> Damage <--Antonym--> Repair <--IsA-- Piece <--RelatedTo--> Chunk 
Pie --AtLocation--> Oven <--AtLocation-- Cake <--RelatedTo--> Item <--RelatedTo--> Board 