Naming systems are specialized databases designed for identifying persons and organizations, locating equipment, and similar tasks. In a perfect world, the user would compose a request using the known attributes, and the system would respond with all matching objects. In practice, however, the request items may be partially wrong or outdated, some may be more important than others, or the system database may be incomplete and partially wrong or outdated. If no perfectly matching item exists, the naming system has to apply increasingly more lax strategies until a suitable item is found. This paper is on a theory of applicable matching strategies.

Several strategies pertaining to the client’s (user’s) present needs exist. For example, the client may prescribe that the naming system use all mandatory attributes (attributes guaranteed to be registered); this strategy is called closed. If no objects are returned, the naming system shall then use the non-mandatory attributes; this strategy is called open. Similarly, the user may order the system to prefer static attributes (which never change their value) over dynamic attributes (where either the database or the user may have outdated information). Technically, a client approximation function is a function from a set of attributes to a subset, such as the set of mandatory attributes.

Correspondingly, several strategies reflect the status of the database. Possible returns all objects that do not conflict with the query. Partial returns all objects that in addition have at least one matching attribute. Exact requires that all attributes in the query match. Unique asks for the single object matching all attributes and returns nothing if more than one such object exists. These four strategies form a preference hierarchy. Technically, a database approximation function is a function from a set of attributes and a set of objects into a set of objects.

Several sets of ordered approximation functions can be combined using a priority between these sets. For example, if (open, closed) gets priority over (possible, partial, exact), then the composition {closed, exact} has the highest priority, followed by {closed, partial} and so on down to {open, possible}. Within a composition, the naming system starts by using only the first component. If this yields too many objects, the set is reduced by the second component; composition essentially yields the intersection.

This systematic approach allows the authors to compare the strategies used in different existing naming systems, to devise new ones, and to reason about their properties. The theory has been used to find inconsistencies in existing naming systems and to design a modified system without these inconsistencies. The authors present several approximation functions at appropriate length. The overall procedure gets somewhat lost in the details.