if a planet has four times the density of earth half the diameter will the gravity be stronger or weaker than earth
Since this is not my area of expertise, I searched Google under the key words "gravity mass" to get this possible source:
http://www.hometrainingtools.com/articles/gravity-mass-weight-science-teaching-tip.html
http://en.wikipedia.org/wiki/Center_of_mass
Consider that the density/mass is greater and you will be closer to the center of the mass. You should be able to come to your own conclusion.
I hope this helps. Thanks for asking.