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.

中文翻译：

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图变换理论与自适应系统中的多值逻辑

图转换理论使用规则来执行图转换。但是，在其中几个都适用的情况下，没有办法在这些不同的转换之间进行选择。这里建议了一种基于对应于不同转换变体的含义值的比较来获得选择的方法。引入束的拓扑与具有相同顶点的图集之间的关系，将逻辑包含在图变换理论中。因此，可以使用特殊类型的蕴涵和这种拓扑的真值集来估计图变换的不同变体。在这种方法中，初始图朝向终端图的最大部分在所选变体中是守恒的。自适应系统的分析使用了一些图文法。自适应系统自主地适应用户需求和操作环境的变化，同时仍保持一些所需的特性。选择此类图转换变体的建议方式可用于在此类系统建模中的不同图文法之间进行选择。这种方法在一些业务流程的模型中进行了说明，在假设流程朝着终端状态变化最小的情况下，会自动选择业务流程适应。