half a mind
half a mind also half a notion {n. phr.}, {informal}
A wish or plan that you have not yet decided to act on; a thought of possibly doing something. — Used after "have" or "with" and before "to" and an infinitive.
I have half a mind to stop studying and walk over to the brook.
Jerry went home with half a mind to telephone Betty.
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Source: A Dictionary of American Idioms
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