Can anyone suggest a good AI library written in C#? I specifically want to use it for ILP so first order logic support is a must.
Have a look at logic engines that work on the .net platform, such as prolog.net or p#. It should be relatively easy to create a c# application that interfaces with a one of these. These examples use prolog, so you might be able to take advantage of other work done in prolog by other people.
For Prolog you have P# and Prolog.Net
Have a look here http://stackoverflow.com/questions/181855/integrating-prolog-with-c
You'll most likely end up having to do some interop with an unmanaged library. This shouldn't be too hard for a well-documented library, however. The Wikipedia article on IPL lists a number of implementations that you might want to take a look at.
I found this site very good. They have books and complete c# code. http://www.heatonresearch.com/