**Disjunction introduction** or **addition** is a simple valid argument form, an immediate inference and a rule of inference of propositional logic. The rule makes it possible to introduce disjunctions to logical proofs. It is the inference that if *P* is true, then *P or Q* must be true.

- Socrates is a man.
- Therefore, either Socrates is a man or pigs are flying in formation over the English Channel.

The rule can be expressed as:

where the rule is that whenever instances of "" appear on lines of a proof, "" can be placed on a subsequent line.

Disjunction introduction is controversial in paraconsistent logic because in combination with other rules of logic, it leads to explosion (i.e. everything becomes provable). See Tradeoffs in Paraconsistent logic.

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**Disjunction Introduction**- Formal Notation

... The

**disjunction introduction**rule may be written in sequent notation where is a metalogical symbol meaning that is a syntactic consequence of in some logical system ...

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