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Elementary Logic with Applications is written for undergraduate logic and logic programming courses. Logic has been applied to a wide variety of subjects such as software engineering and hardware design, to programming and artificial intelligence. In this way, it has served to stimulate the search for clear conceptual foundations. Recently many extensions of classical logic such as temporal, modal, relevance, fuzzy and non-monotonic logics have been widely used in computer science, therefore requiring a new formulation of classic logic which can be modified to yield the effect of non-classical logics. This text aims to introduce classical logic in such a way that one can easily deviate into discussing non-classical logics. It defines a number of different types of logics and the differences between them, starting with the basic notions of the most common logic. Elementary Logic with Applications develops a theorem prover for classical logic in a way that maintains a procedural point of view and presents the reader with the real challenges facing applied logic. Dov Gabbay and Odinaldo Rodrigues have been teaching logic and computer science for many years. Dov Gabbay has written numerous other titles on the subject of logic and is a world authority on non-classical logics. Odinaldo Rodrigues is widely known for his work on logic, belief revision and argumentation. The "Elementary Logic with Applications" course is currently taught at the Department of Informatics, King's College London.