Modus Ponens Inference Rule

A Modus Ponens Inference Rule is a inference rule under which the consequent of a conditional is accepted when the antecedent of the conditional is affirmed.

• AKA: Affirming the Antecedent.
• Context:*
  • It can be expressed as
    • If P, then Q
    • P. Therefore, Q.
• Example(s):
  • All men are mortal. Socrates is a man. Therefore, Socrates is mortal.
• Counter-Example(s):
  • Affirming the Consequent, such as in All men are mortal. Socrates is mortal. Therefore, Socrates is a man..
  • Modus Tollens,
• See: Valid Deductive Argument, Deductive Logic Framework.

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References

2009

• (Wikipedia, 2009) ⇒ http://en.wikipedia.org/wiki/Modus_ponens
  • In classical logic, modus ponendo ponens (Latin for mode that affirms by affirming;[1] often abbreviated to MP or modus ponens) is a valid, simple argument form sometimes referred to as affirming the antecedent or the law of detachment. It is closely related to another valid form of argument, modus tollens or "denying the consequent". Modus ponens is a very common rule of inference, and takes the following form: If P, then Q. P. Therefore, Q.

• http://en.wiktionary.org/wiki/modus_ponens
  • A valid form of argument in which the antecedent of a conditional proposition is affirmed, thereby entailing the affirmation of the consequent.
• CYC Glossary http://www.cyc.com/cycdoc/ref/glossary.html
  • modus ponens: A rule of inference under which, given a knowledge base which contains the formulas "A" and "A implies B", one may conclude "B".
• http://www.philosophy.uncc.edu/mleldrid/logic/logiglos.html
  • Modus ponens: Consists of a conditional statement and one other premise. The second premise affirms the antecedent of the conditional, yielding the consequent as the conclusion: IF (if p then q) AND (p) THEN (q).
• http://www.logic-classroom.info/glossary.htm
  • modus ponens means "a way of constructing;" symbolically: "If p, then q; p; therefore, q." (Study 2; Study 5)
• http://www.economicexpert.com/a/Affirming:the:antecedent.html
  • Affirming the antecedent is a valid argument form which proceeds by affirming the truth of the first part (the "if" part, commonly called the antecedent) of a conditional, and concluding that the second part (the "then" part, commonly called the consequent) is true.
  • If P, then Q. P. Therefore, Q.

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