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In mathematical logic, a formula is a type of abstract object a token of which is a symbol or string of symbols which may be interpreted as any meaningful unit (i.e. a name, an adjective, a proposition, a phrase, a string of names, a string of phrases, etcetera) in a formal language. Two different strings of symbols may be tokens of the same formula. It is not necessary for the existence of a formula that there be any tokens of it. The exact definition of a formula depends on the particular formal language in question.[1] A fairly typical definition (specific to first-order logic) goes as follows Formulas are defined relative to a particular formal language and relation symbols, where each of the function and relation symbols comes supplied with an arity that indicates the number of arguments it takes. Then a term is defined recursively as An atomic formula is one of the form
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