Flag is a type of Sign. Sign is related to Note. Note is related to Scale. Scale is related to Ladder. 
Lower is the opposite of Capital. Capital is related to Place. Place is related to Patch. 
Flag --IsA--> Sign <--RelatedTo--> Note <--RelatedTo--> Scale <--RelatedTo--> Ladder 
Lower <--Antonym--> Capital <--RelatedTo--> Place <--RelatedTo--> Patch 