What does it mean for a system to be consistent or inconsistent?

Since this is not my area of expertise, I searched Google under the key words "system consistent inconsistent" to get this:

http://www.google.com/search?client=safari&rls=en&q=system+consistent+inconsistent&ie=UTF-8&oe=UTF-8

In the future, you can find the information you desire more quickly, if you use appropriate key words to do your own search. Also see http://hanlib.sou.edu/searchtools/.