text: Formal logic uses formal languages to express and analyze arguments.[17] They normally have a very 
  limited vocabulary and exact syntactic rules. These rules specify how their symbols can be combined to 
  construct sentences, so-called well-formed formulas.[18] This simplicity and exactness of formal logic 
  make it capable of formulating precise rules of inference. They determine whether a given argument is 
  valid.[19] Because of the reliance on formal language, natural language arguments cannot be studied 
  directly. Instead, they need to be translated into formal language before their validity can be assessed.[20] 
  
  The term "logic" can also be used in a slightly different sense as a countable noun. In this sense,*a logic*is 
  a logical formal system. Distinct logics differ from each other concerning the rules of inference they 
  accept as valid and the formal languages used to express them.[21] Starting in the late 19th century, many 