An object calculus for geographic databases

Reviewer: William Campbell McGee

Object calculus can be used to query geographic databases. The calculus is based on an object data model, the spatial data model, which gets its spatial flavor through the inclusion of two-dimensional geometric object classes (such as <__?__Pub Fmt italic>point<__?__Pub Fmt /italic>, <__?__Pub Fmt italic>line<__?__Pub Fmt /italic>, and <__?__Pub Fmt italic>area<__?__Pub Fmt /italic>), spatial operators (methods), and topological relationships. Examples of spatial operators are <__?__Pub Fmt italic>line<__?__Pub Fmt /italic>, which returns the line representing the boundary of an area; <__?__Pub Fmt italic>point<__?__Pub Fmt /italic>, which returns the starting and ending points of a line; and <__?__Pub Fmt italic>intersection<__?__Pub Fmt /italic>, which returns the point where two lines intersect. Topological relationships are predicates that have values “true” or “false” when applied to specific geometric objects; an example is the relationship <__?__Pub Fmt italic>in<__?__Pub Fmt /italic>, which is true if one area is wholly contained in another. In the object calculus, i?P i denotes the aggregate of elements i for which the predicate P i is true. A predicate is a well-formed formula composed of atoms and logical operators. An example of an expression in the object calculus is { i? Road i ? <<__?__Pub Caret1><__?__Pub Fmt kern Amount="2pt">( i ,intersection(Interstate 40)), in, Arizona>}, which denotes the set of roads whose intersections with Interstate 40 lie wholly within the state of Arizona. The paper also outlines a method of presenting the results of object calculus queries in the form of maps. Only limited details of this process are given. The authors believe that geographic database query languages that are extensions of standard SQL are too complex and “increase the users' problems of formulating syntactically correct queries.” It appears that the object calculus presented here would not be much better than SQL in this regard, if the example shown above is typical. The authors seem to acknowledge this in the paper summary, where one of the items of further work listed is “the definition of an actual query language corresponding to the formal calculus.” Another item of unfinished business is the use of displayed maps in browsing. These items are needed in order for the object calculus to be of more than routine interest. Readers interested in details of the spatial data model and topological relationships should consult the authors' earlier work [1,2]. The summaries given in this paper omit the definitions of some key concepts, such as dimension, boundary, and intersection.