We extend the theory of initial conflicts in the framework of$$\mathcal {M}$$-adhesive categories to transformation rules with ACs. We first show that for rules with ACs, conflicts are in general neither inherited from a bigger context any more, nor is it possible to find a finite and complete subset of finite conflicts as illustrated for the category of graphs. We define initial conflicts to be special so-called symbolic transformation pairs, and show that they are minimally complete (and in the case of graphs also finite) in this symbolic way. We show that initial conflicts represent a proper subset of critical pairs again. We moreover demonstrate that (analogous to the case of rules without ACs) for each conflict a unique initial conflict exists representing it. We conclude with presenting a sufficient condition illustrating important special cases for rules with ACs, where we do not only have initial conflicts being complete in a symbolic way, but also find complete (and in the case of graphs also finite) subsets of conflicts in the classical sense.
CITATION STYLE
Lambers, L., & Orejas, F. (2020). Initial Conflicts for Transformation Rules with Nested Application Conditions. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 12150 LNCS, pp. 109–127). Springer. https://doi.org/10.1007/978-3-030-51372-6_7
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