Deduction and induction

The difference between deduction, or [deductive logic]?, and induction, or [inductive logic]?, is one of the most important in the elementary study of logic. Here are some definitions:

Deductive logic is the study of arguments that aspire to be, at least, valid.

Inductive logic is the study of arguments that aspire to be, at least, cogent.

The reason these rough definitions are phrased in terms of what the arguments "aspire" to be is that an argument can be properly the subject of deductive logic even though it is not valid or cogent; it can be studied by logic even though it fails to be what it aspires to be. So deduction is concerned with validity; induction is concerned with cogency. In deductive logic one studies forms of arguments such that the conclusion must be true if the premises are true; in inductive logic one studies forms of arguments such that the conclusion is probably true if the premises are true.

Sometimes a distinction is also made between abduction and induction.