A rational reconstruction of the domain of feature structures

Feature structures are employed in various forms in many areas of linguistics. Informally, one can picture a feature structure as a sort of tree decorated with information about constraints requiring that specific subtrees be identical (isomorphic). Here I show that this informal picture of feature structures can be used to characterize exactly the class of feature structures under their usual subsumption ordering. Furthermore, once a precise definition of tree is fixed, this characterization makes use only of standard domain-theoretic notions regarding the information borne by elements in a domain, thus removing (or better, explaining) all apparentlyad hoc choices in the original definition of feature structures. In addition, I show how this characterization can be parameterized in order to yield similar characterizations of various different notions of feature structure, including acyclic structures, structures with appropriateness conditions and structures with apartness conditions (used to model path inequations). The generalizations to other notions of feature structure also emphasize that the construction given here is in fact independent of the application to feature structures.