Chains of Inference:

Now we have to look at how to get an agent to prove a given theorem using various search strategies? Thus we have noted in previous lectures that, there is to specify a search problem, we require to describe the representation language for the artefacts being searched for such the initial state that the goal state or some information about that a goal should look like, and the operators: just how to go from one state to another. 

Here we can state the problem of proving a given theorem from some axioms like a search problem. Means three different specifications give rise to three different ways to solve the problem, by namely forward and backward chaining and by proof contradiction. In this specifications, all the representation language is predicate logic that are not surprisingly so the operators are the rules of inference that allow us to rewrite a set of sentences as another set. However we can think of each state in our search space as a sentence in first order logic. But the operators will traverse this space and finding new sentences. Moreover, we are really only interested in finding a path from the start states to the goal state like this path will constitute a proof. Always notice that there are other ways to prove theorems like exhausting the search for a counterexample and finding none -  in this case but we don't have a deductive proof for the truth of the theorem so we know it is true.