*Modus ponendo tollens*

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Transformation rules |
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Propositional calculus |

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Predicate logic |

* 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 tollens*.

## Overview[edit]

MPT is usually described as having the form:

- Not both A and B
- A
- Therefore, not B

For example:

- 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."^{[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:

## See also[edit]

## References[edit]

**^**Politzer, Guy & Carles, Laure. 2001. 'Belief Revision and Uncertain Reasoning'.*Thinking and Reasoning*. 7:217–234.**^**Stone, Jon R. (1996).*Latin for the Illiterati: Exorcizing the Ghosts of a Dead Language*. London: Routledge. p. 60. ISBN 0-415-91775-1.**^**Lemmon, Edward John. 2001.*Beginning Logic*. Taylor and Francis/CRC Press, p. 61.