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Nowadays, in majority of academic contexts, it has been tried to consider the highest possible level of similarities to the real world. Hence, most of the problems have complicated structures. Traditional methods for solving almost all of the mathematical and optimization problems are inefficient. As a result, meta-heuristic algorithms have been employed increasingly during recent years. In thi...

Abstract: Mathematical logic has two aspects: the syntactic aspect (which, for convenience, we can regard as including the deductive aspect) and the semantic aspect. Peirce’s main influence on today’s mathematical logic lies in his role in the development of first-order logic. Whereas the syntactic aspect of today’s mathematical logic comes to us from Frege, the semantic aspect can, in a reason...

What is mathematical logic? Mathematical logic is the application of mathematical techniques to logic. What is logic? I believe I am following the ancient Greek philosopher Aristotle when I say that logic is the (correct) rearranging of facts to find the information that we want. Logic has two aspects: formal and informal. In a sense logic belongs to everyone although we often accuse others of ...