Abstract
Graph constraints were introduced in the area of graph transformation, in connection with the notion of (negative) application conditions, as a form to limit the applicability of transformation rules. However, we believe that graph constraints may also play a significant role in the area of visual software modelling or in the specification and verification of semi-structured documents or websites (i.e. HTML or XML sets of documents). In this sense, after some discussion on these application areas, we concentrate on the problem of how to prove the consistency of specifications based on this kind of constraints. In particular, we present proof rules for three classes of (increasingly more powerful) graph constraints and show that our proof rules are sound and (refutationally) complete for each class.
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References
AGG.: The AGG, httptfs.cs.tu-berlin.de/agg
Alpuente, M., Ballis, D., Falaschi, M.: Automated Verification of Web Sites Using Partial Rewriting. Software Tools for Technology Transfer 8, 565–585 (2006)
Baldan, P., Corradini, A., Kšnig, B., Lluch-Lafuente, A.: A Temporal Graph Logic for Verification of Graph Transformation Systems. In: Recent Trends in Algebraic Development Techniques, 18th International Workshop, WADT 2006. LNCS, vol. 4409, pp. 1–20. Springer, Heidelberg (2007)
Courcelle, B.: The expression of Graph Properties and Graph Transformations in Monadic Second-Order Logic. In: [18], pp. 313–400 (1997)
Ehrig, H., Ehrig, K., Prange, U., Taentzer, G.: Fundamentals of Algebraic Graph Transformation. Springer, Heidelberg (2006)
Ehrig, H., Ehrig, K., Habel, A., Pennemann, K.-H.: Constraints and Application Conditions: From Graphs to High-Level Structures. In: Ehrig, H., Engels, G., Parisi-Presicce, F., Rozenberg, G. (eds.) ICGT 2004. LNCS, vol. 3256, pp. 287–303. Springer, Heidelberg (2004)
Ehrig, H., Habel, A.: Graph Grammars with Application Conditions: From Graphs to High-Level Structures. In: Rozenberg, G., Salomaa, A. (eds.) The Book of L, pp. 87–100. Springer, Heidelberg (1986)
Ellmer, E., Emmerich, W., Finkelstein, A., Nentwich, C.: Flexible Consistency Checking. ACM Transaction on Software Engineering and Methodology 12(1), 28–63 (2003)
Habel, A., Heckel, R., Taentzer, G.: Graph Grammars with Negative Application Conditions. Fundam. Inform. 26(3/4), 287–313 (1996)
Habel, A., Pennemann, K.-H.: Nested Constraints and Application Conditions for High-Level Structures. In: Kreowski, H.-J., Montanari, U., Orejas, F., Rozenberg, G., Taentzer, G. (eds.) Formal Methods in Software and Systems Modeling. LNCS, vol. 3393, pp. 293–308. Springer, Heidelberg (2005)
Habel, A., Pennemann, K.-H.: Satisfiability of High-Level Conditions. In: Corradini, A., Ehrig, H., Montanari, U., Ribeiro, L., Rozenberg, G. (eds.) ICGT 2006. LNCS, vol. 4178, pp. 430–444. Springer, Heidelberg (2006)
Heckel, R., Wagner, A.: Ensuring Consistency of Conditional Graph Grammars - A Constructive Approach. In: Proceedings SEGRAGRA 1995. Electr. Notes Theor. Comput. Sci., vol. 2, pp. 118–126 (1995)
Jelliffe, R.: “Schematron”, Internet Document (May 2000), http://xml.ascc.net/resource/schematron/
Lack, S., Sobocinski, P.: Adhesive Categories. In: Walukiewicz, I. (ed.) FOSSACS 2004. LNCS, vol. 2987, pp. 273–288. Springer, Heidelberg (2004)
Lambers, L., Ehrig, H., Orejas, F.: Conflict Detection for Graph Transformation with Negative Application Conditions. In: Corradini, A., Ehrig, H., Montanari, U., Ribeiro, L., Rozenberg, G. (eds.) ICGT 2006. LNCS, vol. 4178, pp. 61–76. Springer, Heidelberg (2006)
Nieuwenhuis, R., Rubio, A.: Paramodulation-Based Theorem Proving. In: Robinson, A., Voronkov, A. (eds.) Handbook of Automated Reasoning, Elsevier Science and MIT Press (2001)
Rensink, A.: Representing First-Order Logic Using Graphs. In: Ehrig, H., Engels, G., Parisi-Presicce, F., Rozenberg, G. (eds.) Graph Transformations, Second International Conference, ICGT 2004. LNCS, vol. 3256, pp. 319–335. Springer, Heidelberg (2004)
Rozenberg, G. (ed.): Handbook of Graph Grammars and Computing by Graph Transformation, vol. 1. World Scientific, Singapore (1997)
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Orejas, F., Ehrig, H., Prange, U. (2008). A Logic of Graph Constraints. In: Fiadeiro, J.L., Inverardi, P. (eds) Fundamental Approaches to Software Engineering. FASE 2008. Lecture Notes in Computer Science, vol 4961. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-78743-3_14
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DOI: https://doi.org/10.1007/978-3-540-78743-3_14
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