logic
Logic is often studied by constructing what are commonly called logical systems. A logical system is essentially a way of mechanically listing all the logical truths of some part of logic by means of the application of recursive rules—i.e., rules that can be repeatedly applied to their own output. This is done by identifying by purely formal criteria certain axioms and certain purely formal rules of inference from which theorems can be derived from axioms together with earlier theorems. All of the axioms must be logical truths, and the rules of inference must preserve logical truth. If these requirements are ...(100 of 2985 words)