Modus Ponendo Tollens

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

A ⊻ B – A or B, but not both
A – A [is true]
∴ ¬B – therefore: not B

For example, the following is a valid MPT:

A number is either even or odd (but not both).
x is even.
Therefore x is not odd.

Since contravalence is commutative, this also implies the following:

…
y is odd.
Therefore y is not even.

Name

The name of this inference form can be loosely translated as “form of negation [of a statement] by affirmation [of the alternative]”.

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 Ponendo Tollens and the most important related fallacies:

	Modus ponendo tollens (valid inference)		Denying a Conjunct (fallacy)		Affirming a Disjunct (fallacy)
Premise 1	A ⊻ B (A or B, but not both)		⌐ (A ∧ B) (not both, A and B)		A ∨ B (A oder B)
Premise 2	A	B	⌐A (not A)	⌐B (not B)	A	B
Konklusion	⌐B (not B)	⌐A (not A)	B	A	⌐B (not B)	⌐A (not A)