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mathematical logic:see symbolic logicsymbolic logic
or mathematical logic,
formalized system of deductive logic, employing abstract symbols for the various aspects of natural language. Symbolic logic draws on the concepts and techniques of mathematics, notably set theory, and in turn has contributed to
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a branch of logic that makes use of mathematical methods.
The use of formal languages with an exact syntax and precise semantics that unambiguously define the meaning of formulas is characteristic of mathematical logic. The need for such a logic arose in the early 20th century in connection with the intensive development of the foundations of mathematics, the emergence of set theory in which antinomies had been discovered, the refinement of the concept of an algorithm, as well as with other profound and fundamental problems of mathematical science. The importance of mathematical logic for science as a whole, however, is not exhausted by its mathematical applications, since all sciences require good reasoning and methods of proof. This is why mathematical logic can rightfully be called logic in its most recent development.
A. A. MARKOV