A system of logic developed solely in terms of rules of inference. In the place of axioms there are only rules, saying what can be derived from any given assumption. However, there will be rules for ‘discharging’ assumptions, leading to results derivable from anything at all, and these are the theorems of the system. The rule of conditional proof is one such rule. Such systems are useful for three reasons: (i) they conform better than axiomatic systems to the view that logic is about inference, rather than about a special set of ‘logical truths’; (ii) they avoid the arbitrariness of choosing just one set of logical truths as axioms; and (iii) they are often easier to manipulate.
Philosophy dictionary. Academic. 2011.