However, natural deduction systems have no logical axioms; they compensate by adding additional rules of inference that can be used to manipulate the logical connectives in formulas in the proof.
12.
In the following example of a propositional calculus, the transformation rules are intended to be interpreted as the inference rules of a so-called " natural deduction system ".
13.
In particular, tabular natural deduction systems, which are very convenient for practical theorem-proving in propositional calculus and predicate calculus, were applied by and for teaching introductory logic in textbooks.
14.
The historical development of tabular-layout natural deduction systems, which are rule-based, and which indicate antecedent propositions by line numbers ( and related methods such as vertical bars or asterisks ) includes the following publications.
15.
He said that the special role of the excluded middle in the classical natural deduction system NK is removed in the classical sequent calculus system LK . He said that the sequent calculus LJ gave more symmetry than natural deduction NJ in the case of intuitionistic logic, as also in the case of classical logic ( LK versus NK ).
16.
According to Prawitz ( 1965 ) : " The calculi of sequents can be understood as meta-calculi for the deducibility relation in the corresponding systems of natural deduction . " And furthermore : " A proof in a calculus of sequents can be looked upon as an instruction on how to construct a corresponding natural deduction . " In other words, the assertion symbol is part of the object language for the sequent calculus, which is a kind of meta-calculus, but simultaneously signifies deducibility in an underlying natural deduction system.
