Modus ponens

Anglais

Modus ponens

Modus ponens, a short form of modus ponendo ponens (Latin for "the way that affirms by affirming"; generally abbreviated to MP or modus ponens[1]) is a rule of inference in propositional logic.[2] It is also called implication elimination as this inference rule can be used to replace the condition by the consequence in the arguments. It can be summarized as "(1) (P implies Q) and (2) (P) are asserted to be true, and therefore Q must be true." The history of modus ponens goes back to antiquity.[3]

Modus ponens is closely related to another valid form of argument, modus tollens. Both have apparently similar but invalid forms such as affirming the consequent, denying the antecedent, and evidence of absence. Constructive dilemma is the disjunctive version of modus ponens. Hypothetical syllogism is closely related to modus ponens and sometimes thought of as "double modus ponens."