Clearing the fog is half-smart (9)

I believe the answer is:

demisting

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'clearing the fog' is the definition.
Although both the answer and definition are present participle verbs, I don't understand how one could define the other.

'half-smart' is the wordplay.
'half' becomes 'demi' (prefix as in 'demigod').
'smart' becomes 'sting' (both can mean to burn or hurt).
'demi'+'sting'='DEMISTING'

'is' acts as a link.

Can you help me to learn more?

I've seen this clue in The Daily Express.

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