Reference : Satisfaction, Restriction and Amalgamation of Constraints in the Framework of M-Adhes...
Scientific journals : Article
Engineering, computing & technology : Computer science
Satisfaction, Restriction and Amalgamation of Constraints in the Framework of M-Adhesive Categories
Schölzel, Hanna [TU Berlin, Germany]
Ehrig, Hartmut [TU Berlin, Germany]
Maximova, Maria [TU Berlin, Germany]
Gabriel, Karsten [TU Berlin, Germany]
Hermann, Frank mailto [University of Luxembourg > Interdisciplinary Centre for Security, Reliability and Trust (SNT) > >]
Electronic Proceedings in Theoretical Computer Science [=EPTCS]
Open Publishing Association
Yes (verified by ORBilu)
[en] 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

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