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Refers to an exclusive disjunction (“or”-statement). Contravalence can be paraphrased as “either A, or B, but not both”.

For example:

For dessert, you can have fruit salad or ice cream [but not both].


A contravalence is a statement that is true if exactly one of the two sub-statements is true, i.e. in this case if there is fruit for dessert or if there is ice cream. Unlike in an adjunction (inclusive disjunction), the overall expression is not true if both partial statements are true, i.e. if both, ice cream and fruit are served.

A B A ⊻ B
true true false
true false true
false true true
false false false

Colloquial use

Although there is no specific word for an exclusive “or” in English, people often try to clarify this meaning by constructions such as “either … or …”, or by emphasizing: “… but not both”. This is often awkward and does not exactly represent the meaning of the logical expression.

Occasionally, the neologism “xor” (“exclusive or ”), originating from information sciences, is occasionally used in written language to denote a contravalence.

In Latin, the word “aut” stands for an exclusive “or”. This term is also occasionally used to denote contravalence.

Logical symbol

On this website, the symbol is used for contravalence. In other places, you may also find or instead. These symbols are all pronounced “aut  ”.

An alternative is the term “xor”, as explained above (pronounced: “ex-or ”).

See also

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