Generalized encoding of description spaces and its application to typed feature structures

This paper presents a new formalization of a unification- or join-preserving encoding of partially ordered sets that more essentially captures what it means for an encoding to preserve joins, generalizing the standard definition in AI research. It then shows that every statically typable ontology in the logic of typed feature structures can be encoded in a data structure of fixed size without the need for resizing or additional union-find operations. This is important for any grammar implementation or development system based on typed feature structures, as it significantly reduces the overhead of memory management and reference-pointer-chasing during unification.