On the Classification of Natural Deduction Calculi

In 1934 Jaśkowski and Gentzen independently published their groundbreaking works on Natural Deduction. The aim of this paper is to provide some criteria for division of the diversity of existing systems on some natural subcategories and to show that despite the differences all these systems are descendants of original systems of Jaśkowski and Gentzen. Three criteria are discussed:The kind of items which are building-blocks of the proof.The format of proof.The kind of rules.The first leads to the division of ND into two main classes: F-systems working on formulas and S-systems working on sequents. The second distinguishes between T-systems with tree-proofs and L-systems with linear proofs. Finally, the third leads to several minor divisions in the main categories.