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Every possible extension of an extensible constraint can be added in one step. Multiple similar extensions between the same elements can be prohibited by further NACs for the production. These are not vital structural constraints but save from redundancy.

There must be one production for every possible extension of an extensible constraint:

Construction P_extensiblee: The right-hand side of the production is an extension graph of E. The left-hand side is created by the vertices of the right-hand side, an NAC for each edge of the right-hand side, and, if p_max is not empty, an NAC consisting of the constraint's maximal embedding graph p_max such that the constraint is unified with the constraint of the right-hand side (NAC without the constraint itself). In the same way as the last NAC, further NACs have to be introduced for all other constraint vertices of the extension graph to prevent from exceeding the constraints' p_max graphs.

Production P_Machinee in the figure below shows an example for an extension of the Machine object constraint.

For every extension of a constraint, there must be a production to remove the extension. The requirement req_min can be satisfied by providing an additional PAC with the p_base graph for each constraint:

Construction P_extensibler: The production's left-hand side is similar to the extension graph of E, including a PAC that contains the p_base graph, such that the constraint is unified with the constraint of the extension graph (PAC without the constraint itself). In the same way as the PAC, further PACs have to be introduced for all other constraint vertices of the extension graph to prevent from falling below the constraints' p_base graphs. The right-hand side is the left-hand side without the PACs and the edges.

Production P_Machiner in the figure above shows an example for the reduction of the Machine object constraint.

req_p is satisfied, as P_extensibler is the reversal of P_extensiblee without its NACs, and as the PACs cannot endanger the applicability as the existence of the p_base graphs is ensure by req_min.

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Last update:
May 20, 2001 by Alexander Nareyek