Definition:Proof Rule
From ProofWiki
Definition
A proof rule is a rule in natural deduction which allows one to work out the truth values of statement forms from other statement forms.
The terms rule of derivation and transformation rule, when used in this context, mean the same thing.
Structure of a Proof Rule
A proof rule has a structure, as follows:
- Definition: This specifies what the proof rule actually does. Note the careful use of can and may in the definition:
- Can implies that it is possible to achieve something based on the structure of the system which is being constructed.
- May implies that this is what this particular proof rule is allowing you to do.
- Abbreviation: When deriving a sequent, it is convenient to use a precisely defined shorthand to indicate which rule is being applied at a particular point.
- Deduced from: The truth value of a result which is being deduced by a particular proof rule depends on a specific set of premises, or assumptions made during the course of derivation. This pool of assumptions will vary depending on what the proof rule is and what previously derived result or results the proof rule depends on.
- Discharged assumptions: This specifies which, if any, assumptions have been discharged, that is, are no longer considered to contribute to the truth value of the result being derived.
- Depends on: This specifies the result from which the proof rule directly derives its result.
