In the three (or generally n)- valued logic the truth values (apart from negation) for connectors differ from one logic to another (there are thousands 3-valued logics). So what are the rules (criterion) that one should follow to define an n-valued logic which makes sense. Is it the application scopes only which control the definition process?
Usually application (or theoretical justification). Many-valued logics began mostly to be able to address problems like the Sorites paradox, vagueness, etc. Fuzzy logic, an infinitely many-valued logic, was designed to deal with language. Quantum logic was obviously designed to reflect quantum mechanics (which violates the LNC and non tertium datur). Theoretically, one can define some n-valued logic anyway one chooses. However, if one does, one shouldn't expect others to pay much heed to it.
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