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Creation Deductive Inferences :
Here we have shown how knowledge can be represented in first-order logic or how rule-based expert systems expressed in logic can be constructed and use to represent the knowledge. So here we look at how to take some known facts regarding a domain and deduce new facts from them. Thus this will, in terms of, enable agents to prove things, that is., just to start with a set of statements in which we believe to be true axioms and deduce whether another statement or can say theorem is true or may not. Firstly, We will first look at how to tell if there a sentence in propositional logic is true or false. Here this will suggest some equivalences between propositional sentences, that allow us to rewrite sentences to other sentences that mean the same thing, regardless of the truth or meaning of the single propositions they contains. According to above discussion these are reversible inferences, in fact in that deduction can be applied either way. So after that we look at propositional and first-order inference rules in generally, that can be enable us deduce new sentences where we know that some certain things are true, that may not be reversible.
Asymptotic Notations These notations are used for evaluating functions. Assume we have two functions f(n) and g(n) defined on real numbers, Theta Notation Big Notation
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