Disjunction introduction
Disjunction introduction or Addition is a simple argument form, an immediate inference and a valid rule of inference of propositional logic. The rule makes it possible to introduce disjunctions to logical proofs. It is the inference that if A is true, then A or B must be true.
It can be expressed in formal language as:
The argument form has one premise, A, and an unrelated proposition, B. From the premise it can be logically concluded that either A or B is true.
Here is an example of such an argument:
- Socrates is a man.
- Therefore (either or both of) Socrates is a man, or pigs are flying in formation over the English Channel.
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.