Modus ponendo tollens
|Rules of inference|
|Rules of replacement|
Modus ponendo tollens (Latin: "mode that by affirming, denies") is a valid rule of inference for propositional logic, sometimes abbreviated MPT. It is closely related to modus ponens and modus tollens. It is usually described as having the form:
- Not both A and B
- Therefore, not B
- Ann and Bill cannot both win the race.
- Ann won the race.
- Therefore, Bill cannot have won the race.
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."
In logic notation this can be represented as:
Based on the Sheffer Stroke (alternative denial), "|", the inference can also be formalized in this way: