  The purpose of logic is to characterize the difference between valid and invalid arguments. A logical system for a language is a set of axioms and rules designed to prove exactly the valid arguments statable in the language. Creating such a logic may be a difficult task. The logician must make sure that the system is sound, i.e. that every argument proven using the rules and axioms is in fact valid. Furthermore, the system should be complete, meaning that every valid argument has a proof in the system. Demonstrating soundness and completeness of formal systems is a logician’s central concern. 