## Covering Collections

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The function #$TheCovering can be used to express the "covering" of a (set or) collection by other (sets or) collections. (For more information on functions, see the documentation section on Non-Atomic Terms.) If a collection is covered by a set of other collections, then any instance of the covered collection must also be an instance of at least one of the members of the covering set.

To specify a covering, we use the predicate #$covering, which relates a (set or) collection to a set of (sets or) collections that cover it. We indicate the collections in the covering set by making them arguments of the function #$TheCovering. This function creates a set -- here, an actual #$Set-Mathematical -- that contains the covering subsets. Consider the following example:

         (#$covering Z (#$TheCovering D E F))

The collection Z is covered by the collections D, E, and F, which all belong to the set created by #$TheCovering. (Note that #$isa is not the predicate used to relate D, E, and F to the covering set. Since this is a mathematical set rather than a collection, the appropriate relation is #$elementOf.)

Note that the members of the covering set may or may not be subsets of the covered set -- D is a spec of Z, but E and F are not. Note also that the members of the covering set may share elements: R is an instance of both E and F.

The constant S is in a disallowed situation, since it is an instance of Z but it is not an instance of either D, E, or F.

Here is an example usage of #$covering in the KB:

        (#$covering #$CreationOrDestructionEvent
                    (#$TheCovering #$CreationEvent #$DestructionEvent))

The somewhat awkward-sounding constant #$CreationOrDestructionEvent is in fact a useful collection because it is used to constrain the arguments for predicates which apply to events which are either creation events, destruction events, or both.

Last Update: 03/28/2002