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## Harmony Based on EquivalenceApproaches based on generalised eliminations or generalised introductions maintain that these generalised rules have a distinguished status, so that harmony can be defined with respect to them. An alternative way would be to explain what it means that given introductions Such an approach is described for propositional logic in Schroeder-Heister [66]. Its idea is to translate the meaning of a connective [
Its introduction meaning is ∀ are equivalent in IPC2, the introduction and elimination rules for && are in harmony with each other. Further examples are discussed in Schroeder-Heister [66]. The translation into IPC2 presupposes, of course, that the connectives inherent in IPC2 are already taken for granted. Therefore, this approach works properly only for generalised connectives different from the standard ones. As it reduces semantical content to what can be expressed by formulas of IPC2, it was called a 'reductive' rather than 'foundational' approach. As described in Schroeder-Heister [63] this can be carried over to a framework that employs higher-level rules, making the reference to IPC2 redundant. However, as the handling of quantified rules in this framework corresponds to what can be carried out in IPC2 for implications, this is not a presupposition-free approach either. The viability of both approaches hinges on the notion of equivalence, that is, the idea that meanings expressed by equivalent propositions (or rules in the foundational approach), one representing the content of introduction-premisses and the other one representing the content of eliminationconclusions, is sufficient to describe harmony. |

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