Introducing second-order spider diagrams for defining regular languages

Proceedings - 2010 IEEE Symposium on Visual Languages and Human-Centric Computing, VL/HCC 2010

Volumn , Issue , 2010, Pages 159-167

  Chapman, Peter ^a   Stapleton, Gem ^a  

^a UNIVERSITY OF BRIGHTON   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

DIAGRAMMATIC LOGIC; FIRST-ORDER; PRIMARY CONTRIBUTION; REGULAR LANGUAGES; RESEARCH EFFORTS; SECOND ORDERS; SECOND-ORDER LOGIC; SPIDER DIAGRAMS; SYMBOLIC LOGIC;

RESEARCH;

EID: 79952053124     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/VLHCC.2010.30     Document Type: Conference Paper

References (20)

1. J. Büchi. Weak second order arithmetic and finite automata. Zeitschrift für mathematische Logik und Grundlagen der Mathematik, 6:66-92, 1960.
2. R. Cohen and J. Brzozowski. Dot-depth of star-free events. Journal of Computer and System Science, 5:1-16, 1971.
3. F. Dau and P. Ekland. A diagrammatic reasoning system for the description logic ACL. Journal of Visual Languages and Computing, 19(5):539-573, 2008.
4. A. Delaney and G. Stapleton. On the descriptional complexity of a diagrammatic notation. In 13th International Conference on Distributed Multimedia Systems, Visual Languages and Computing, pages 195-202, 2007.
5. A. Delaney and G. Stapleton. Spider diagrams of order. In Visual Languages and Logic, volume 274 of CEUR, pages 27-39, 2007.
6. A. Delaney, G. Stapleton, J. Taylor, and S. Thompson. A diagrammatic characterisation of commutative star-free regular languages. in preparation.
7. A. Delaney, J. Taylor, and S. Thompson. Spider diagrams of order and a hierarchy of star-free regular languages. In 5th International Conference on the Theory and Application of Diagrams, LNCS, pages 172-187. Springer, 2008.
8. H.-D. Ebbinghaus and J. Flum. Finite Model Theory. Springer-Verlag, 1991.
9. C. Gurr. Aligning syntax and semantics in formalisations of visual languages. In Proceedings of IEEE Symposia on Human-Centric Computing Languages and Environments, pages 60-61. IEEE Computer Society Press, 2001.
10. J. Howse, G. Stapleton, and J. Taylor. Spider diagrams. LMS Journal of Computation and Mathematics, 8:145-194, 2005.
11. S. Kent. Constraint diagrams: Visualizing invariants in object oriented modelling. In Proceedings of OOPSLA97, pages 327-341. ACM Press, October 1997.
12. A. Mateescu and A. Salomaa. Formal languages: an introduction and a synopsis. In Handbook of formal languages, vol. 1: word, language, grammar, pages 1-39. Springer-Verlag New York, Inc., New York, NY, USA, 1997.
13. A. Shimojima. Inferential and expressive capacities of graphical representations: Survey and some generalizations. In Proceedings of 3rd International Conference on the Theory and Application of Diagrams, volume 2980 of LNAI, pages 18-21, Cambridge, UK, 2004. Springer.
14. S.-J. Shin. The Logical Status of Diagrams. Cambridge University Press, 1994.
15. G. Stapleton and A. Delaney. Evaluating and generalizing constraint diagrams. Journal of Visual Languages and Computing, 19(4):499-521, 2008.
16. G. Stapleton and J. Masthoff. Incorporating negation into visual logics: A case study using Euler diagrams. In Visual Languages and Computing 2007, pages 187-194. Knowledge Systems Institute, 2007.
17. G. Stapleton, S. Thompson, J. Howse, and J. Taylor. The expressiveness of spider diagrams. Journal of Logic and Computation, 14(6):857-880, December 2004. (Pubitemid 40009826)
18. N. Swoboda and G. Allwein. Using DAG transformations to verify Euler/Venn homogeneous and Euler/Venn FOL heterogeneous rules of inference. Journal on Software and System Modeling, 3(2):136-149, 2004.
19. W. Thomas. Classifying regular events in symbolic logic. Journal of Computer and System Sciences, 25:360-376, 1982. (Pubitemid 13491113)
20. B. Trahtenbrot. Finite automata and the logic of monadic predicates. Sibirskij Mat. Zhurnal, 3:103-131, 1962.