Fact refers to something that actually happens or can be proved true. For example,“‘NATO has now decided to enforce the no-fly zone over Libya. We’re taking action as part of the broad international effort to protect civilians from attacks of Gadhafi,’ Anders Fogh Rasmussen told CNN’s Wolf Blitzer”.
Influence is statement reasoned from Facts.“NATO has reached an agreement to take over the no-fly zone in Libya from the United States “in a couple of days,” NATO’s secretary general said Thursday.”
Theory is a Fact-less statement however applicable to a definite range of cases.“There is no perfect formula for military intervention. It must be used sparingly — not in Bahrain or Yemen, even though we condemn the violence against protesters in both countries.”
(Quotes are taken from CNN and NY Times)