Just guessing / offering personal opinion... such words would rarely make sense in source code.

What would a function called "believe" do?

I can imagine such function names in, say, artificial intelligence projects, but even there used (probably) in a loose way. I suspect few web applications or iPhone games or flight control programs would be doing any "believing", real or imaginary.

Of the words you suggested, "sense" seems most likely to appear in real use, as robotic software and such may be literally accessing sensors.