Logic is the study of formal languages for propositions and truth. Logics are used both as a foundation of mathematics and as specification languages in mathematics and computer science. Since logic is intricately intertwined with the nature of mathematics, the question how to represent logics in our minds is a constant challenge to our understanding. And only when it is understood can we begin to answer the corresponding question about logic translations. At the same time logics are used to a large extent in computer science to reason about both mathematics and software systems.