Satisfaction, Restriction and Amalgamation of Constraints in the Framework of M-Adhesive Categories

Hanna Schölzel
(Institut für Softwaretechnik und Theoretische Informatik, Technische Universität Berlin, Germany)
Hartmut Ehrig
(Institut für Softwaretechnik und Theoretische Informatik, Technische Universität Berlin, Germany)
Maria Maximova
(Institut für Softwaretechnik und Theoretische Informatik, Technische Universität Berlin, Germany)
Karsten Garbriel
(Institut für Softwaretechnik und Theoretische Informatik, Technische Universität Berlin, Germany)
Frank Hermann
(University of Luxembourg, Interdisciplinary Centre for Security, Reliability and Trust )

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.

In Ulrike Golas and Thomas Soboll: Proceedings Seventh ACCAT Workshop on Applied and Computational Category Theory (ACCAT 2012), Tallinn, Estonia, 01/04/2012, Electronic Proceedings in Theoretical Computer Science 93, pp. 83–104.
Published: 21st August 2012.

ArXived at: http://dx.doi.org/10.4204/EPTCS.93.5 bibtex PDF
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