Logic is the science of logical relations. It studies the conditions of valid inference. The term "logic" was first used by Alexander of Aphrodisius (2nd century A.D.) for the logical writings of Aristotle which were called the Organnon, or instrument of science. Inference is the logical relation which involves the passage from one or more statements that are called the premises to another statement called the conclusion. When the conclusion follows from the premises necessarily, the method of inference is called deduction, and the method of inference is called deductive inference. The branch of logic that formulates the rules of deductive inference is called deductive logic. If the conclusion follows from the premises with a degree of probability less than certainty, the method of inference is called induction and the method of inference is called inductive inference. The branch of logic that formulates the rules of inductive inference is called inductive logic. Logic not only studies the conditions of valid inference but also of invalid inference. These invalid reasonings are called fallacies, from the Latin fallacia ("deceit","trick", or "fraud").
The development of logic began historically with the Greeks philosophers and spans a period of 2500 years in the West. The history of logic is usually divided into classical logic and modern logic. Classical logic centers on the development of deductive and inductive inference which was first developed by Aristotle. Modern logic began in the West in 19th century with the work of George Boole. Modern logic (sometimes called Symbolic Logic) divides the science of logic into the Sentential Logic (also called Propositional Calculus) and Class Logic (also called Predicate Calculus). The foundations of Sentential Logic was laid by Frege and Peirce. Sentential Logic is a formalization of the logical relations "and", "or", "not", and "if-then", which holds between sentences or propositions. Symbols are used to represent these relations and the letters "p", "q", "r", etc. to stand for propositions. The definition of these relations and derivation of theorems or formulas are expressed by the use of matrices called Truth Tables. In these tables the truth values of compound sentences are determined by the truth values of the constitutents.