Sign Function is a term sometimes used as a general equivalent of a sign.
The reason for preferring the term sign function over sign is that the term sign function suggests something dynamic and (according to Umberto Eco) mobile.
Everything that acts as a sign or is taken as a sign is such, thanks to some function (for example, the function of standing in front of something other than it, or of mediating between two things that would otherwise be completely separate or unrelated). And in the same thing, it could play different roles in different contexts and even in the same context.
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