Modus Tollendo Ponens

Also abbreviated MTP. One of the elementary (valid) logical conclusion figures. It is based on a disjunction and has the form:

A ∨ B – (A or B)
¬A – (not A)
∴ B – (therefore B)

For example, the following is a valid MTP:

Today will be rain or fog.
There is no rain today.
Therefore there will be fog today.

Name

The name of this form can be freely translated as “method of infering an affirmative sstatement by denying”.

As with other forms of logical reasoning, there are several fallacies that can on incorrect application of the MPT:

The following table compares the Modus tollendo ponens and the most important related fallacies:

	Modus tollendo ponens (valid inference)		Denying a Conjunct (fallacy)		Affirming a Disjunct (fallacy)
Premise 1	A ∨ B (A or B)		A ⊻ B (A or B, but not both)		A ∨ B (A or B)
Premise 2	⌐A (not A)	⌐B (not B)	⌐A (not A)	⌐B (not B)	A	B
Conclusion	B	A	B	A	⌐B (not B)	⌐A (not A)