文章基本信息

标题：Satisfaction, Restriction and Amalgamation of Constraints in the Framework of M-Adhesive Categories
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作者：Hanna Schölzel ; Hartmut Ehrig ; Maria Maximova 等
期刊名称：Electronic Proceedings in Theoretical Computer Science
电子版ISSN：2075-2180
出版年度：2012
卷号：93
页码：83-104
DOI：10.4204/EPTCS.93.5
出版社：Open Publishing Association
摘要：Application conditions for rules and constraints for graphs are well-known in the theory of graph transformation and have been extended already to M-adhesive transformation systems. According to the literature we distinguish between two kinds of satisfaction for constraints, called general and initial satisfaction of constraints, where initial satisfaction is deﬁned for constraints over an initial object of the base category. Unfortunately, the standard deﬁnition of general satisfaction is not compatible with negation in contrast to initial satisfaction.
Based on the well-known restriction of objects along type morphisms, we study in this paper restriction and amalgamation of application conditions and constraints together with their solutions. In our main result, we show compatibility of initial satisfaction for positive constraints with restriction and amalgamation, while general satisfaction fails in general.
Our main result is based on the compatibility of composition via pushouts with restriction, which is ensured by the horizontal van Kampen property in addition to the vertical one that is generally satisﬁed in M-adhesive categories.