- Disjunction introduction
Rules of inference Propositional calculus Modus ponens (A→B, A ⊢ B)
Modus tollens (A→B, ¬B ⊢ ¬A)
Modus ponendo tollens (¬(A∧B), A ⊢ ¬B)
Conjunction introduction (A, B ⊢ A∧B)
Simplification (A∧B ⊢ A)
Disjunction introduction (A ⊢ A∨B)
Disjunction elimination (A∨B, A→C, B→C ⊢ C)
Disjunctive syllogism (A∨B, ¬A ⊢ B)
Hypothetical syllogism (A→B, B→C ⊢ A→C)
Constructive dilemma (A→P, B→Q, A∨B ⊢ P∨Q)
Destructive dilemma (A→P, B→Q, ¬P∨¬Q ⊢ ¬A∨¬B)
Biconditional introduction (A→B, B→A ⊢ A↔B)
Biconditional elimination (A↔B ⊢ A→B)
Predicate calculus Universal generalization
- Therefore, A or B.
or in logical operator (sequent) notation:
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, or both are 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.
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