3 kinds of commonsense -

1) Embedded in the structure of language itself - 

This has been explained in the case of the "write a letter"-example sent before (a few days ago). A letter is a physical paper body. You can cut it, throw it, fold it. But how can you "write it"? How can you "write a physical body?" But this shows that language itself has taken shape so as to include this commonsense, wherein writing a letter means writing text/contents on a piece of paper.

2) Nothing to do with any Linguistic theory / (Not embedded in the structure of language) - 

This is the conventional commonsense in AI literature. "The police threw tear gas at the demonstrators because they feared violence". Who is 'they' here? Identifying this has nothing to do with any Linguistic theory, but your commonsense knowledge of the world about policemen, demonstrations and demonstrators etc.

3) Having both of the above aspects - 

Consider this sentence - "This is that shoe's sock". 

When we say this, why are we using the " apostrophe 's' "? It is because the commonsense that A particular shoe belongs to A particular sock and the other to another (i.e. the right one to the right and the left one to the left) is absorbed in the way language is formed - apostrophe 's' indicates the association of a shoe with its right sock. This is one kind of commonsense (type 1).

The other kind of commonsense here is that some real information that is assumed and well-known is hidden. In the literal utterance "shoe's sock" it is meant "the sock worn in the leg that very shoe is worn in". This is the conventional (type 2) commonsense involved here.