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A feature structure is a rooted graph, which is built similar to a feature tree. Every feature tree is a feature structure. Every feature structure can be unfolded into a feature tree. When doing so, node equality is lost but structural equality is preserved.
Feature constraints can be given an alternative semantics. Rather than interpreting a variable as a feature trees, one may interpreted a variable as a node in a feature structure. This alternative interpretation could be used without affecting the notions of solvability, solved forms, or unification.
In other words, for a feature structure only the information it represents matters but how structural equality is expressed: either by node equality or by the structural equality of trees. Node equality is an implementation detail which can be used to express structural equality. Only structural equality matters. We built our logics on the notion of feature trees rather than on feature structures in order to not use node equality (called ``structure sharing'' in Pollard/Sag) as a basic metaphor in our explanations.
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