Independence An axiom is independent iff it can t be derived from the other axioms by the rules of inference An axiom schema is independent iff not every instance of it is a theorem of the system obtained by deleting from the set of axioms all instances of the schema in question A rule of inference is independent if there is a theorem which cant be derived without using that rule of inference Logic in Computer Science - p. 12/17Independence • An axiom is independent iff it can’t be derived from the other axioms by the rules of inference. • An axiom schema is independent iff not every instance of it is a theorem of the system obtained by deleting from the set of axioms all instances of the schema in question. • A rule of inference is independent if there is a theorem which can’t be derived without using that rule of inference. Logic in Computer Science – p.12/17