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Adjunction (logic)

Denotes an inclusive disjunction (“or”). Adjunction can be para­phrased as “either A, or B, or both”.

For example:

Today there is going to be fog, or rain [or both].

An adjunction is true when at least one of the two sub-expressions is true, that is, when it is raining or when there is fog. Unlike with contra­valences (exclusive disjunctions), an ad­junction also evalu­ates to true, if both sub-expressions are true – that is, if it is both foggy and raining.

Other names

  • Inclusive “or”

Truth table

An adjunction is true if at least one of the sub-statements is true.

A B A ∨ B
true true true
true false true
false true true
false false false

Colloquial use

In many languages – including English – no distinction is made between inclusive and exclusive “or”. Unless it is indicated otherwise, normal colloquial use of the word should assume an inclusive meaning (i.e., an adjunction), since this is by far the most common usage.

In Latin, however, there are explicitly different expressions for the two disjunctions, with the word vel standing for an inclusive “or”.

Logical symbol

In the context of this website, the symbol (pronounced: “vel ”) is used as a sign for inclusive disjunction. In other publications, symbols like +, or , or others are used with the same meaning.

See also

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