Conversion, Obversion, and Contraposition

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