Sound Rules of Inference
Here are some examples of sound rules of inference. Each can be shown
to be sound once and for all using a truth table. The left
column contains the premise sentence(s), and the right column contains
the derived sentence. We write each of these derivations as A |- B ,
where A is the premise and B is the derived sentence.
| Name | Premise(s) | Derived Sentence |
|---|
| Modus Ponens | A, A => B | B |
| And Introduction | A, B | A ^ B |
| And Elimination | A ^ B | A |
| Double Negation | ~~A | A |
| Unit Resolution | A v B, ~B | A |
| Resolution | A v B, ~B v C | A v C |