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TU Berlin

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Publications Prof. Hartmut Ehrig (TFS)

Satisfaction, Restriction and Amalgamation of Constraints in the Framework of M-Adhesive Categories
Zitatschlüssel SEM+12
Autor Schölzel, H. and Ehrig, H. and Maximova, M. and Gabriel, K. and Hermann, F.
Buchtitel Proc. Seventh ACCAT Workshop on Applied and Computational Category Theory (ACCAT'12)
Jahr 2012
Zusammenfassung Application conditions for rules and constraints for graphs are well-known in the theory of graph transformation and have been extended already toM-adhesive transformation systems. Concerning constraints we distinguish according to the literature between two kinds of satisfaction, 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. This is based on a result concerning compatibility of compositions via pushouts with restriction, where the proof requires the horizontal van Kampen property, in contrast to the vertical one required forM-adhesive categories.
Download Bibtex Eintrag [1]
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