Visual Multiset Rewriting: Applications to Diagram Parsing and Reasoning

  • Paolo Bottoni
  • Bernd Meyer
  • Francesco Parisi Presicce
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2235)


Diagrammatic notations, such as Venn diagrams, Petri-Nets and finite state automata, are in common use in mathematics and computer science. While the semantic domain of such systems is usually well formalized, the visual notation itself seldom is, so that they cannot be used as valid devices of formal reasoning. A complete formalization of such notations requires the construction of diagram systems with rigorously defined syntax and semantics. We discuss how diagram specification can be interpreted as multiset rewriting and, based on this, how it can be formalized in linear logic. We discuss the power of our approach through an illustration of its possible extension with reflective capabilities to manage negative conditions, and through the identification of a class of diagrammatic transformations which can be directly expressed in our framework.


  1. [ACP93]
    J.-M. Andreoli, P. Ciancarini, and R. Pareschi. Interaction abstract machines. In G. Agha, P. Wegner, and A. Yonezawa, editors, Research Directions in Concurrent Object-Oriented Programming, pages 257–280. MIT Press, Cambridge, MA, 1993.Google Scholar
  2. [AFP96]
    J.-M. Andreoli, S. Freeman, and R. Pareschi. The coordination language facility: Coordination of distributed objects. Theory and Practice of Object Systems, 2:77–94, 1996.CrossRefGoogle Scholar
  3. [AP91]
    J.-M. Andreoli and R. Pareschi. Linear objects: Logical processes with built-in inheritance. New Generation Computing, 9:445–473, 1991.CrossRefGoogle Scholar
  4. [BBMP96]
    U.M. Borgho., P. Bottoni, P. Mussio, and R. Pareschi. A systemic metaphor of multi-agent coordination in living systems. In Proc. European Simulation Multiconference (ESM’96), pages 245–253, 1996.Google Scholar
  5. [BBMP97]
    U.M. Borgho., P. Bottoni, P. Mussio, and R. Pareschi. Reflective agents for adaptive workflows. In Proc. 2nd Int. Conf. on the Practical Application of Intelligent Agents and Multi-Agent Technology (PAAM’ 97), pages 405–420, 1997.Google Scholar
  6. [BCM99]
    P. Bottoni, M.F. Costabile, and P. Mussio. Specification and dialogue control of visual interaction through visual rewriting systems. ACM Transactions on Programming Languages and Systems, 21:1077–1136, 1999.CrossRefGoogle Scholar
  7. [BMMP01]
    P. Bottoni, B. Meyer, K. Marriott, and F. Parisi Presicce. Deductive parsing of visual languages. In Int. Conf. on Logical Aspects of Computational Linguistics, Le Croisic, France, June 2001.Google Scholar
  8. [BMST99]
    R. Bardohl, M. Minas, A. Schürr, and G. Taentzer. Application of graph transformation to visual languages. In H. Ehrig, G. Engels, H.-J. Kreowski, and G. Rozenberg, editors, Handbook of Graph Grammars and Computing by Graph Transformation, volume 2, pages 105–180. World Scientific, 1999.Google Scholar
  9. [BPPS00]
    P. Bottoni, F. Parisi Presicce, and M. Simeoni. From formulae to rewriting systems. In H. Ehrig, G. Engels, H.-J. Kreowsky, and G. Rozenberg, editors, Theory and Application of Graph Transformations, pages 267–280. Springer, Berlin, 2000.Google Scholar
  10. [CMR+97]
    A. Corradini, U. Montanari, F. Rossi, H. Ehrig, R. Heckel, and M. Lowe. Algebraic approaches to graph transformation-Part I: basic concepts and double pushout approach. In G. Rozenberg, editor, Handbook of Graph Grammars and Computing by Graph Transformation, volume 1, pages 163–245. World Scientific, 1997.Google Scholar
  11. [EHK+97]
    H. Ehrig, R. Heckel, M. Kor., M. Löwe, L. Ribeiro, A. Wagner, and Corradini. Algebraic approaches to graph transformation II: Single pushout approach and comparison with double pushout approach. In G. Rozenberg, editor, Handbook of Graph Grammars and Computing by Graph Transformation, Volume 1: Foundations, chapter 4. World Scientific, 1997.Google Scholar
  12. [Gir87]
    J.-Y. Girard. Linear logic. Theoretical Computer Science, 50:1–102, 1987.MATHCrossRefMathSciNetGoogle Scholar
  13. [Gir91]
    J.-Y. Girard. Linear logic: A survey. Technical report, Int. Summer School on Logic and Algebra of Specification, 1991.Google Scholar
  14. [Haa98]
    V. Haarslev. A fully formalized theory for describing visual notations. In K. Marriott and B. Meyer, editors, Visual Language Theory, pages 261–292. Springer, New York, 1998.Google Scholar
  15. [HM91]
    R. Helm and K. Marriott. A declarative specification and semantics for visual languages. Journal of Visual Languages and Computing, 2:311–331, 1991.CrossRefGoogle Scholar
  16. [HMO91]
    R. Helm, K. Marriott, and M. Odersky. Building visual language parsers. In ACM Conf. Human Factors in Computing, pages 118–125, 1991.Google Scholar
  17. [HP94]
    J. Harland and D. Pym. A uniform proof-theoretic investigation of linear logic programming. Journal of Logic and Computation, 4(2):175–207, April 1994.MATHCrossRefMathSciNetGoogle Scholar
  18. [HPW96]
    J. Harland, D. Pym, and M. Winikoff. Programming in Lygon: An overview. In Algebraic Methodology and Software Technology, LNCS 1101, pages 391–405. Springer, July 1996.CrossRefGoogle Scholar
  19. [Man98]
    V. Manca. String rewriting and metabolism: A logical perspective. In G. Paun, editor, Computing with Bio-Molecules, pages 36–60. Springer-Verlag, Singapore, 1998.Google Scholar
  20. [Mar94]
    K. Marriott. Constraint multiset grammars. In IEEE Symposium on Visual Languages, pages 118–125. IEEE Computer Society Press, 1994.Google Scholar
  21. [Mey97]
    B. Meyer. Formalization of visual mathematical notations. In M. Anderson, editor, AAAI Symposium on Diagrammatic Reasoning (DR-II), pages 58–68, Boston/MA, November 1997. AAAI Press, AAAI Technical Report FS-97-02.Google Scholar
  22. [Mey00]
    B. Meyer. A constraint-based framework for diagrammatic reasoning. Applied Artificial Intelligence, 14(4):327–344, 2000.CrossRefGoogle Scholar
  23. [Mil95]
    D. Miller. A survey of linear logic programming. Computational Logic, 2(2):63–67, December 1995.Google Scholar
  24. [MM00]
    K. Marriott and B. Meyer. Non-standard logics for diagram interpretation. In Diagrams 2000: International Conference on Theory and Application of Diagrams, Edinburgh, Scotland, September 2000. Springer. To appear.Google Scholar
  25. [MMW98]
    K. Marriott, B. Meyer, and K.B. Wittenburg. A survey of visual language specification and recognition. In K. Marriott and B. Meyer, editors, Visual Language Theory, pages 5–85. Springer, 1998.Google Scholar
  26. [RS95]
    A. Repenning and T. Sumner. Agentsheets: A medium for creating domainoriented visual languages. IEEE Computer, 28(3):17–26, March 1995.Google Scholar
  27. [SCS94]
    D.C. Smith, A. Cypher, and J. Sporer. Kidsim: Programming agents without a programming language. Comm. ACM, 37(7):55–67, July 1994.CrossRefGoogle Scholar
  28. [Shi95]
    S.-J. Shin. The Logical Status of Diagrams. Cambridge University Press, Cambridge, 1995.Google Scholar
  29. [Tan91]
    T. Tanaka. Definite clause set grammars: A formalism for problem solving. Journal of Logic Programming, 10:1–17, 1991.CrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Paolo Bottoni
    • 1
  • Bernd Meyer
    • 2
  • Francesco Parisi Presicce
    • 1
  1. 1.Dipartimento di Scienze dell’ InformazioneUniversità La Sapienza di RomaRoma
  2. 2.School of Computer Science & Software EngineeringMonash UniversityAustralia

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