The difference between Formal language and Formal system

When used as nouns, formal language means a generally finite set of possible strings (called sentences) made of symbols (from a symbol set called the alphabet) along with rules constraining how the symbols can be used, whereas formal system means the grouping of a formal language and a set of inference rules and/or axioms.

check bellow for the other definitions of Formal language and Formal system

  1. Formal language as a noun (computing theory):

    A generally finite set of possible strings (called sentences) made of symbols (from a symbol set called the alphabet) along with rules constraining how the symbols can be used.

  1. Formal system as a noun (logic):

    The grouping of a formal language and a set of inference rules and/or axioms.

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