Because we think of feature structures as representing partial information, the question immediately arises as to whether the notion of total information makes sense in this framework and if so, what its relation to partial information might be. Our notions of “total” information in this chapter are decidedly relative in the sense that they are only defined with respect to a fixed type inheritance hierarchy and fixed appropriateness conditions.

Before tackling the more complicated case of feature structures, we consider the first-order terms. First-order terms can be ordered by subsumption. The maximal elements in this ordering are the ground terms, a ground term being simply a term without variables. It is well known that the semantics of logic programming systems and even first-order logic can be characterized by restricting attention to the collection of ground terms, the so-called Herbrand Universe. The reason this is true is that every first-order term is equivalent to the meet of the collection of its ground extensions (Reynolds 1970). Thus any first-order term is uniquely determined by its ground extensions. It is also interesting to note that as a corollary, a term subsumes a second term just in case its set of ground instantiations is strictly larger than the set of ground instantiations of the second term. In this chapter, we consider whether or not we can derive equivalent results for feature structures. One motivation for deriving such results is that they make life much easier when it comes time to characterize the behavior of feature structure unification-based phrase structure grammars and logic programming systems. Unfortunately, we achieve only limited success.