1. syllogism – logical reasoning from inarguable premises; the conclusion is unarguable if the syllogism is structured correctly.
Example:  Because Socrates is human, he is mortal. Major Premise: All humans are mortal (irrefutable generalization) Minor Premise: Socrates is a human Conclusion: Therefore, Socrates is mortal

2. enthymeme – logical reasoning with one premise left unstated; instead of having an irrefutable general truth for major premise, it is an assumption, statement, or proposition that the writer presumes and the audience accepts.
Example: [Because gravity exists,] my pencil will fall when I drop it. [Major Premise: Gravity exists. (a theory)] Minor Premise: My pencil exists in gravity. Conclusion: Therefore, my pencil falls when I drop it.

3. faulty syllogism – when one or both of the premises are refutable or untrue
Major Premise: All women are wise. (refutable) Minor Premise: Ms. Wallingford is a woman. Conclusion: Therefore, Ms. Wallingford is wise.
Major Premise: Poisonous snakes have spots. Minor Premise: That snake has spots. Conclusion: Therefore, that snake is poisonous.

4. deductive reasoning – reasoning that begins with a general principle and concludes with a specific instance that demonstrates the general principle
Example of Deduction
major premise: All tortoises are vegetarians
minor premise: Bessie is a tortoise
conclusion: Therefore, Bessie is a vegetarian
Deductive reasoning is commonly found in the natural sciences or “hard” sciences, less so in everyday arguments
Occasionally, everyday arguments do involve deductive reasoning:
Example: “Two or more persons are required to drive in the diamond lane. You don’t have two or more persons. Therefore you may not drive in the diamond lane”
commonly associated with “formal logic.”
involves reasoning from known premises, or premises presumed to be true, to a certain conclusion.
the conclusions reached are certain, inevitable, inescapable.

5. inductive reasoning – reasoning that begins by citing a number of specific instances or examples and then shows how collectively they constitute a general principle
Example of Induction
Boss to employee: “Biff has a tattoo of an anchor on his arm. He probably served in the Navy.”
Inductive reasoning is found in the courtroom, the boardroom, the classroom, and throughout the media
Most, but not all everyday arguments are based on induction
Examples: The “reasonable person” standard in civil law, and the “beyond a reasonable doubt” standard in criminal law
commonly known as “informal logic,” or “everyday argument”
involves drawing uncertain inferences, based on probabilistic reasoning.
the conclusions reached are probable, reasonable, plausible, believable