formal logic

noun
the branch of logic concerned exclusively with the principles of deductive reasoning and with the form rather than the content of propositions.

Origin:
1855–60

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World English Dictionary
formal logic
 
n
1.  Compare philosophical logic Also called: symbolic logic the study of systems of deductive argument in which symbols are used to represent precisely defined categories of expressions
2.  a specific formal system that can be interpreted as representing a fragment of natural argument

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Encyclopedia Britannica
Encyclopedia

formal logic

the abstract study of propositions, statements, or assertively used sentences and of deductive arguments. The discipline abstracts from the content of these elements the structures or logical forms that they embody. The logician customarily uses a symbolic notation to express such structures clearly and unambiguously and to enable manipulations and tests of validity to be more easily applied. Although the following discussion freely employs the technical notation of modern symbolic logic, its symbols are introduced gradually and with accompanying explanations so that the serious and attentive general reader should be able to follow the development of ideas

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Encyclopedia Britannica, 2008. Encyclopedia Britannica Online.
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Example sentences
The benefit of formal logic is that it is pure syntax.
Any formal logic in these pieces would exist solely in the minds of misguided
  listeners.
While logical reasoning skills are related to success in science, the
  relationship between thought and formal logic is not clear.
Symbols without referents can be manipulated according to the laws of formal
  logic.
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