The difference between Formal system and Syntax
When used as nouns, formal system means the grouping of a formal language and a set of inference rules and/or axioms, whereas syntax means a set of rules that govern how words are combined to form phrases and sentences.
check bellow for the other definitions of Formal system and Syntax
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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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Syntax as a noun:
A set of rules that govern how words are combined to form phrases and sentences.
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Syntax as a noun (computing, countable):
The formal rules of formulating the statements of a computer language.
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Syntax as a noun (linguistics):
The study of the structure of phrases, sentences and language.