User:Lord Farin/Backup/Definition:Natural Deduction

Natural Deduction is a technique for deducing valid sequents from other valid sequents by applying precisely defined proof rules, each of which themselves are either "self-evident" axioms or themselves derived from other valid sequents, by a technique called logical inference.

Proof Rules
The following rules are often treated as the axioms of PropLog. Some of them are "obvious", but they still need to be stated formally. Others are more subtle.

This is not the only valid analysis of this subject. There are other systems which use other (often fewer) proof rules, but these ones are straightforward and are easy to get to grips with.

Note the careful use of "can" and "may" in the axiom definitions that are included here.


 * "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.

Note that each proof rule depends on a pool of assumptions, which needs to be specified for each proof rule.

Also note that premises of an argument are considered to be assumptions themselves.