Appear is a synonym of Become. Occur is a type of Become. Occur is a synonym of Arise. Arise is a synonym of Mount. 
Being is related to Able. Able is a different concept from Impossible. 
Appear <--Synonym--> Become <--IsA-- Occur <--Synonym--> Arise <--Synonym--> Mount 
Being <--RelatedTo--> Able <--DistinctFrom--> Impossible 