Multi-valued logic in graph transformation theory and self-adaptive systems

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.