Definition
Inference Rule
An inference rule is a syntactic rule that describes how to derive a new formula (the conclusion) from one or more existing formulas (the premises). It is typically written as:
where are the premises and is the conclusion.
Properties
- Soundness: A rule is sound if, whenever the premises are true, the conclusion is also true.
- Completeness: A set of rules is complete if every logical consequence can be derived using the rules.
Syntactic Nature
Inference rules are purely syntactic; they operate on the form of the formulas rather than their meaning (semantics).