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In this paper, we use the following notation expressing constraints about the existence of PJ elements. This notation is adopted from the DL community. The meaning of these notations is that there may exist at least (at most, exactly) n different PJ elements such that p() holds.
The definitions for `at most' and `exactly' are identical except that for `at most' and for `exactly' m = n has to hold.
Furthermore, we assume the following basic predicates for primitive objects:
The unary predicates for primitive objects are used to define auxiliary predicates: