obverted

Obverted refers to a logical operation applied to categorical propositions. It involves changing a proposition by changing its quality from affirmative to negative, or vice versa, and at the same time changing the predicate term to its complement. The complement of a term is everything that is not that term. For example, if the term is "dog," its complement is "non-dog."

The process of obversion follows specific rules. For an A proposition (all S are P), obverting it results in an E proposition (no S are not-P). For an E proposition (no S are P), obverting it results in an A proposition (all S are not-P). For an I proposition (some S are P), obverting it results in an O proposition (some S are not not-P). For an O proposition (some S are not P), obverting it results in an I proposition (some S are not-P).

Obversion is a valid inference rule in traditional logic, meaning that if a proposition is true, its obverted form will also be true, and vice versa. It is a way of rephrasing a statement while preserving its truth value. This operation is useful in simplifying propositions, converting them into standard forms, or making them more amenable to other logical manipulations. It is a fundamental tool in Aristotelian logic and forms part of the square of opposition.