Graph transformation theory uses rules to perform a graph transformation. However, there is
no a way to choose between such different transformations in the case where several of them
are applicable. A way to get the choice is suggested here based on the comparing of the values
of implications which correspond to different transformation variants. The relationship
between the topos of bundles, and the set of graphs with the same vertices, is introduced
to include logic into graph transformation theory. Thus, one can use the special type of
implication and the truth-values set of such a topos to estimate different variants of graph
transformations. In this approach, the maximal part of the initial graph towards the terminal
one is conserved in the chosen variant. Analysis of self-adaptive systems uses some graph
grammars. Self-adaptive systems autonomously perform an adaptation to changes both in
user needs and in their operational environments, while still maintaining some desired properties.
The suggested way to choose such graph transformation variants may be used to
make a choice between different graph grammars in such systems modeling. This approach
is illustrated in a model of some business processes, that result in the automated choice of
the business process adaptation under the assumption that the process changes are minimal
towards the terminal state.