Formal logic

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.

Source

http://www.britannica.com/topic/formal-logic