Segerberg presented a general completeness proof for propositional logics. For this purpose, a Natural Deduction system was defined in a way that its rules were rules for an arbitrary boolean operator in a given propositional logic. Each of those rules corresponds to a row on the operator s truth-table. In the first part of this thesis we extend Segerbergs idea to finite-valued propositional logic and to non-deterministic logic. We maintain the idea of defining a deductive system whose rules correspond to rows of truth-tables, but instead of having n types of rules (one for each truth-value), we use a bivalent representation that makes use of the technique of separating formulas as defined by Carlos Caleiro and João Marcos. The system defined has so many rules it might be laborious to work with it. We believe that a sequent calculus system defined in a similar way would be more intuitive. Motivated by this observation, in the second part of this thesis we work out translations between Sequent Calculus and Natural Deduction, searching for a better bijective relationship than those already existing.