Modus ponendo tollens
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:
- Stone, Jon R. 1996. Latin for the Illiterati: Exorcizing the Ghosts of a Dead Language. London, UK: Routledge:60.
- Politzer, Guy & Carles, Laure. 2001. 'Belief Revision and Uncertain Reasoning'. Thinking and Reasoning. 7:217-234.
- Lemmon, Edward John. 2001. Beginning Logic. Taylor and Francis/CRC Press: 61.