Logic

Excerpted from Wikipedia:

Logic is the formal systematic study of the principles of valid inference and correct reasoning. Logic is used in most intellectual activities, but is studied primarily in the disciplines of philosophy, mathematics, semantics, and computer science. Logic examines general forms which arguments may take, which forms are valid, and which are fallacies. In philosophy, the study of logic figures in most major areas: epistemology, ethics, metaphysics. In mathematics, it is the study of valid inferences within some formal language. Logic is also studied in argumentation theory.

For more information see Wikipedia: Logic

Excerpted from Wikipedia:

Inductive reasoning, also known as induction or inductive logic, is a kind of reasoning that constructs or evaluates propositions that are abstractions of observations of individual instances of members of the same class. It is commonly construed as a form of reasoning that makes generalizations based on individual instances. In this sense it is often contrasted with deductive reasoning.

For more information see Wikipedia: Inductive Reasoning

Excerpted from Wikipedia:

Deductive reasoning, also called deductive logic, is reasoning which constructs or evaluates deductive arguments. Deductive arguments are attempts to show that a conclusion necessarily follows from a set of premises or hypotheses. A deductive argument is valid if the conclusion does follow necessarily from the premises, i.e., the conclusion must be true provided that the premises are true. A deductive argument is sound if it is valid and its premises are true. Deductive arguments are valid or invalid, sound or unsound. Deductive reasoning is a method of gaining knowledge. An example of a deductive argument:

All men are mortal
Socrates is a man
Therefore, Socrates is mortal

The first premise states that all objects classified as "men" have the attribute "mortal". The second premise states that "Socrates" is classified as a man – a member of the set "men". The conclusion states that "Socrates" must be mortal because he inherits this attribute from his classification as a man.

For more information see Wikipedia: Deductive Reasoning

Using logic does not guarantee valid conclusions. These links lead to discussions regarding the conditions for sound and unsound logical arguments.

Logically Sound Argument: Creating a sound logical arguments applies to deductive reasoning. But, keep in mind that, if the reasoner used induction to formulate his premises, he must subject his inductive reasoning to rigorous scrutiny.
Logical Errors: I have borrowed a map of logical errors (along with descriptions) from Karl Albrecht to provide a framework for gathering examples of logical errors in economics.