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Admissible equivalence systems

Whenever a logic is the set of theorems of some deductive system, where the latter has an equivalence system, the behavioral theorems of the logic can be determined by means of that equivalence system. In general, this original equivalence system may be too restrictive, because it su ces to check behavioral theorems by means of any admissible equivalence system (that is an equivalence system of the small- est d...