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Satisfaction, Restriction and Amalgamation of Constraints in the Framework of M-Adhesive Categories
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.Comment: In Proceedings ACCAT 2012, arXiv:1208.430
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