Defining the natural language and its gradient phenomena force us to look for formal tools that can represent the bases of a grammar with degrees of grammaticality. The mathematical and formal models are often used in linguistics. And yet, fuzzy logic has not received all the attention it deserves as a tool to explain the natural language processing. Here, we show the theoretical bases that have led us to treat the natural language (NL) inputs gradually. The basis of fuzzy logic for NL are explained here as a tool capable of defining non-discrete values, therefore gradual or fuzzy. A Property Grammar will give the rules of the fuzzy grammar.
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