I believe it should be:
fink install swi-prolog The package name is swi-prolog. Fink will take care of getting the right version. You may also find apt-cache helpful:
apt-cache search prolog EDIT: I think the issue is that swi-prolog and gprolog are in the unstable section. The Fink FAQ explains how to turn unstable on. After following those instructions, you should be able to install them.
yap comes up in apt-cache because it is in the stable section. However, it's not installed. If you choose to use that, you still have to do:
fink install yap