In logic, natural deduction is an approach to proof theory that attempts to provide a deductive system which is a formal model of logical reasoning as it "naturally" occurs. This approach is in contrast to axiomatic systems which use axioms.
One version of natural deductive logic has no axioms. System L, developed by E.J. Lemmon, has only nine primitive rules that govern the syntax of a proof.
The nine primitive rules of system L are
In system L,...
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In logic, natural deduction is an approach to proof theory that attempts to provide a deductive system which is a formal model of logical reasoning as it "naturally" occurs. This approach is in contrast to axiomatic systems which use axioms.
One version of natural deductive logic has no axioms. System L, developed by E.J. Lemmon, has only nine primitive rules that govern the syntax of a proof.
The nine primitive rules of system L are
In system L, a proof has a definition with the following conditions:
If no premise is given, the sequent is called theorem. Therefore, the definition of a theorem in system L is:
An example of the proof of a sequent (Modus Tollendo Tollens in this case):
An example of the proof of a sequent (a theorem in this case):
Each rule of system L has its own requirements for the type of input(s) or entry(es) that it can accept and has its own way of treating and calculating the assumptions used by its inputs.
Natural deduction grew out of a context of...
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