Full Idea
A 'natural deduction system' will have no logical axioms but may rules of inference.
Gist of Idea
A 'natural deduction system' has no axioms but many rules
Source
Peter Smith (Intro to Gödel's Theorems [2007], 09.1)
Book Reference
Smith,Peter: 'An Introduction to Gödel's Theorems' [CUP 2007], p.59
A Reaction
He contrasts this with 'Hilbert-style systems', which have many axioms but few rules. Natural deduction uses many assumptions which are then discharged, and so tree-systems are good for representing it.