have half a mind to (do something)
To have an inclination or intention that is moderate, irresolute, or indefinite (but often one that was motivated by a specific unpleasant experience). My flight home was so terrible, I have half a mind to write a letter to the airline company and complain. We set out on the road with only half a mind as to where we would go!
have half a mind to do something
If you say that you have half a mind to do something, you are thinking about doing it or threatening to do it, although you probably will not do it. I was wet and weary and had half a mind to curl up on the hillside and wait for the rescue helicopter. I have half a mind to file a lawsuit against her. Note: You can also say that someone is of half a mind to do something. I was of half a mind to leave, but it was late so I stayed.
have a (or a good or half a) mind to do something
be very much inclined to do something.have a mind to do something
want to do or achieve something: He could pass the exam easily, if he really had a mind to.I have a mind to find out the truth behind all this.