Proof by contradiction, Computer Engineering

Proof by Contradiction:

Now for forward chaining and backward chaining both have drawbacks. But another approach is to think about proving theorems by contradiction. So we can say these are very common in mathematics: mathematicians simply some axioms, after do this make an assumption. In fact after some complicated mathematics there they have shown like an axiom is false or something derived from the axioms that did not involve the assumption is false. So as the axioms are irrefutably correct because the assumption they made must be false. However the assumption is inconsistent with the axioms of the theory. Just To need this for a particular theorem that they want to prove is true but they negate the theorem statement for use this as the assumption they are going to show is false. But as the negated theorem must be false, then their original theorem must be true. Bingo! 

Now we can program our reasoning agents to do just the same. Just to simplify this as a search problem, then therefore we have to say that as the axioms of our theory and the negation of the theorem that we want to prove are the initial search states. Thus if we can deduce the false statement from our axioms so the theorem we were trying to prove will the false statement from our axioms and the theorem we were trying to prove will indeed have been proven. Because not only can we use all our rules of inference also have a goal to aim for.

Posted Date: 1/11/2013 6:08:52 AM | Location : United States







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