Modus ponendo tollens (MPT;[1] Latin: "mode that denies by affirming")[2] is a valid rule of inference for propositional logic.
It is closely related to modus ponens and modus tollendo ponens.
MPT is usually described as having the form: For example: As E. J. Lemmon describes it: "Modus ponendo tollens is the principle that, if the negation of a conjunction holds and also one of its conjuncts, then the negation of its other conjunct holds.
"[3] In logic notation this can be represented as: Based on the Sheffer Stroke (alternative denial), "|", the inference can also be formalized in this way: Modus ponendo tollens can be made stronger by using exclusive disjunction instead of non-conjunction as a premise: