Conversion is the inference in which the subject and predicate are interchanged. In modern logic it is only valid for the **E** and **I** propositions. The valid converse is logically equivalent to the original proposition. In traditional logic, the **A** proposition has a converse by limitation which is the subaltern of the invalid **A**-converse; i.e., the corresponding **I** proposition. The converse by limitation is implied by the original but is not (usually) equivalent to it.

ORIGINAL | CONVERSE | VALID? | BY LIMITATION | |

All S are P | All P are S | no | Some P are S | |

No S are P | No P are S | yes | ||

Some S are P | Some P are S | yes | ||

Some S are not P | Some P are not S | no |

Obversion is the inference in which the quality of the proposition is changed and the predicate is interchanged with its complement. It is valid for all four forms. The obverse is logically equivalent to the original proposition.

ORIGINAL | OBVERSE | VALID? | ||

All S are P | No S are nonP | yes | ||

No S are P | All S are nonP | yes | ||

Some S are P | Some S are not nonP | yes | ||

Some S are not P | Some S are nonP | yes |

Contraposition is the inference in which the subject is interchanged with the complement of the predicate and the predicate is interchanged with the complement of the subject. In modern logic it is only valid for the **A** and **O** propositions. The valid contrapositive is logically equivalent to the original proposition. In traditional logic, the **E** proposition has a contrapositive by limitation which is the subaltern of the invalid **E**-contrapositive; i.e., the corresponding **O** proposition. The contrapositive by limitation is implied by the original but is not (usually) equivalent to it.

ORIGINAL | CONTRAPOSITIVE | VALID? | BY LIMITATION | |

All S are P | All nonP are nonS | yes | ||

No S are P | No nonP are nonS | no | Some nonP are not nonS | |

Some S are P | Some nonP are nonS | no | ||

Some S are not P | Some nonP are not nonS | yes |