*Abstract:*

Standard concepts of initial and final algebra semantics are generalised in a modular hierarchical manner. The resulting relative formalism allows a unified view on the relationship between initial and final algebra semantics and gives a dualised notion of consistency. Using this, a modular hierarchical approach to proof by consistency is taken by which only top-level equations need be considered at any level. The formalism also allows non-homogeneous specification schemes and different proof methods at each level.

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