Graphical Consistency Constraints

In AGG graphical consistency constraints can be defined.
A graphical consistency constraint is a total injective morphism $c : P \to C$, the left graph $P$ is called premise and the right graph $C$ is called conclusion. A graphical consistency constraint is satisfied by a graph $G$, if for all total injective morphisms $p : P \to G$ there is a total injective morphisms $q : C \to G$ such that $q \circ c = p$. If $CC$ is a set of graphical consistency constraints, we say that $G$ satisfies $CC$, if $G$ satisfies all constraints in $CC$.

A graphical consistency constraint (GCC) can be created choosing menu item New Atomic Constraint of pop-up menu GraGra. A GCC can contain more arbitrary conclusions. The default size of conclusions is equal to 1. A new conclusion can be created using menu item New Conclusion of pop-up menu GCC.
The left and right graphs and the morphism of a GCC are edited like a rule. The premise is only allowed to have constant values and variables as attribute values.
In AGG graphical consistency constraints are placed at the end of the grammar tree and marked by icon A.
We use the sample application StateCharts as an example of graphical consistency constraints.
In Figures 38 - 43 we can see a graphical consistency constraint with six conclusions. They describe the possible relations between two state nodes S or rather a state node S and state chart node SC.
Please note, in AGG a graphical consistency constraint with $n$ conclusions is constructed as a set of $n$ morphisms $P \to C$, where $P$ is the same premise graph and $C$ is always a different conclusion graph.

Figure 38: Sabs_absS conclusion of GraphConstraint

Figure 39: SaSaSC conclusion of GraphConstraint

Figure 40: LoopSaSaS conclusion of GraphConstraint

Figure 41: LoopSaSCaS conclusion of GraphConstraint

Figure 42: Sabs_absSC conclusion of GraphConstraint

Figure 43: SCabs_absS conclusion of GraphConstraint

It is sufficient that at least one conclusion of a GCC is satisfied. We use a consistency condition ( logical formula like this: ($\neg{a}$) ) to make the GCC meaningful. We want to say, that this GraphConstraint is not allowed in graphs of StateCharts. Consistency conditions will be described in the next section.