Graduated Errors in Approximate Queries Using Hierarchies and Ordered Sets

Abstract

Often, qualitative values have an ordering, such as (very-short, short, medium-height, tall) or a hierarchical level, such as (The-World, Europe, Spain, Madrid), which are used by people to interpret mistakes and approximations among these values. Confusing Paris with Madrid yields an error smaller than confusing Paris with Australia, or Paris with Abraham Lincoln. And the “difference” between very cold and cold is smaller than that between very cold and warm. Methods are provided to measure such confusion, and to answer approximate queries in an “intuitive” manner. Examples are given. Hierarchies are a simpler version of ontologies, albeit very useful. Queries have a blend of errors by order and errors by hierarchy level, such as “what is the error in confusing very cold with tall?” or “give me all people who are somewhat like (John (plays baseball) (travels-by water-vehicle) (lives-in North-America)).” Thus, retrieval of approximate objects is possible, as illustrated here.