In logic, an inverse is a type of conditional sentence which is an immediate inference made from another conditional sentence.
More specifically, given a conditional sentence of the form
, the inverse refers to the sentence
Since an inverse is the contrapositive of the converse, inverse and converse are logically equivalent to each other.
, and since the double negation of any statement is equivalent to the original statement in classical logic, the inverse of the inverse is logically equivalent to the original conditional
The inverse and the converse of a conditional are logically equivalent to each other, just as the conditional and its contrapositive are logically equivalent to each other.
For example, the sentence cannot be inferred from the sentence because in the case where it's not raining, additional conditions may still prompt Sam and Jack to meet at the movies, such as: In traditional logic, where there are four named types of categorical propositions, only forms A (i.e., "All S are P") and E ("All S are not P") have an inverse.
To find the inverse of these categorical propositions, one must: replace the subject and the predicate of the inverted by their respective contradictories, and change the quantity from universal to particular.
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