It is said that there is no agreement of the exact definition of logic. Considering that formal logic, symbolic logic and mathematical logic all have a different understanding of the sign, then, it would be difficult to come to any agreement.
The fact that in mathematical logic signs are joined in a numerical abstract relation divorced from reality it cannot be applied directly to it (although most people think it is the purest language). And symbolic logic tries to work with grammar, again abstract and different depending on the language.
The only real description of logic is therefore one which is based on the physical without being related to the signifier. We need to separate the signifier and signified in a meaningful logical way.
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