Deductive Inferences - Artificial intelligence:
We have described how knowledge can be represented in first-order logic, and how in logic rule-based expert systems expressed can be used and constructed. Now, we look at how to take home known facts regarding a domain and deduce new facts from them. In turn, this will enable agents to prove things, for example, to begin with a set of statements we believe to be true (axioms) and deduce whether another statement (theorem) is true or false. We will first look at how to tell whether a sentence in propositional logic is true or false. This will advise some equivalences among propositional sentences, which let us to rewrite sentences to other sentences which mean the similar thing, regardless of the truth or meaning of the specific propositions they contains. These are reversible inferencesthat can be applied in deduction either way. In general, we then look at propositional and first-order inference rules, which enable us deduce new sentences if we know that certain things are true, and which cannot be reversible.