Visual mathematics: Diagrammatic formalization and proof

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 5144 LNAI, Issue , 2008, Pages 478-493

  Howse, John ^a   Stapleton, Gem ^a  

^a UNIVERSITY OF BRIGHTON   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

ADMINISTRATIVE DATA PROCESSING; ALGEBRA; ARTIFICIAL INTELLIGENCE; CLASSIFICATION (OF INFORMATION); COMPUTER NETWORKS; INFORMATION MANAGEMENT; KNOWLEDGE MANAGEMENT; LINGUISTICS; MANAGEMENT INFORMATION SYSTEMS; MATHEMATICAL TECHNIQUES; NUMBER THEORY;

INTERNATIONAL CONFERENCES; MATHEMATICAL CONCEPTS; SYMBOLIC COM-PUTATION;

FORMAL LOGIC;

EID: 51049110536     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-540-85110-3_39     Document Type: Conference Paper

References (29)

1. Barwise, J., Etchemendy, J.: Language Proof and Logic. CSLI (1999)
2. Chow, S.: Generating and Drawing Area-Proportional Euler and Venn Diagrams. PhD thesis. University of Victoria (2007)
3. Dau, F.: http://www.dr-dau.net/eg_readings.shtml (2006)
4. Fish, A., Flower, J., Howse, J.: The semantics of augmented constraint diagrams. Journal of Visual Languages and Computing 16, 541-573 (2005)
5. Flower, J., Howse, J.: Generating Euler diagrams. In: Proceedings of 2nd International Conference on the Theory and Application of Diagrams, Georgia, USA, April 2002, pp. 61-75. Springer, Heidelberg (2002)
6. Flower, J., Masthoff, J., Stapleton, G.: Generating readable proofs: A heuristic approach to theorem proving with spider diagrams. In: Blackwell, A.F., Marriott, K., Shimojima, A. (eds.) Diagrams 2004. LNCS (LNAI), vol. 2980, pp. 166-181. Springer, Heidelberg (2004)
7. Giaquinto, M.: Visual Thinking in Mathematics. Clarendon Press (2007)
8. Gurr, C.: Aligning syntax and semantics in formalisations of visual languages. In: Proceedings of IEEE Symposia on Human-Centric Computing Languages and Environments, pp. 60-61. IEEE Computer Society Press, Los Alamitos (2001)
9. Gurr, C., Tourlas, K.: Towards the principled design of software engineering diagrams. In: Proceedings of 22nd International Conference on Software Engineering, pp. 509-518. ACM Press, New York (2000)
10. Howse, J., Schuman, S.: Precise visual modelling. Journal of Software and Systems Modeling 4, 310-325 (2005)
11. Howse, J., Stapleton, G., Taylor, J.: Spider diagrams. LMS Journal of Computation and Mathematics 8, 145-194 (2005)
12. Jamnik, M.: Mathematical Reasoning with Diagrams. CSLI (2001)
13. Kent, S.: Constraint diagrams: Visualizing invariants in object oriented modelling. In: Proceedings of OOPSLA 1997, pp. 327-341. ACM Press, New York (1997)
14. Kim, S.-K., Carrington, D.: Visualization of formal specifications. In: 6th Asia Pacific Software Engineering Conference, pp. 102-109. IEEE Computer Society Press, Los Alamitos (1999)
15. Mutton, P., Rodgers, P., Flower, J.: Drawing graphs in Euler diagrams. In: Blackwell, A.F., Marriott, K., Shimojima, A. (eds.) Diagrams 2004. LNCS (LNAI), vol. 2980, pp. 66-81. Springer, Heidelberg (2004)
16. Nelson, R.: Proofs without Words: Exercises in Visual Thinking, vol. 1. The Mathematical Association of America (1997)
17. Rodgers, P., Zhang, L., Stapleton, G., Fish, A.: Embedding wellformed euler diagrams. In: 12th International Conference on Information Visualization. IEEE, Los Alamitos (2008)
18. Shimojima, A.: Inferential and expressive capacities of graphical representations: Survey and some generalizations. In: Blackwell, A.F., Marriott, K., Shimojima, A. (eds.) Diagrams 2004. LNCS (LNAI), vol. 2980, pp. 18-21. Springer, Heidelberg (2004)
19. Shin, S.-J.: The Logical Status of Diagrams. Cambridge University Press, Cambridge (1994)
20. Shin, S.-J.: The Iconic Logic of Peirce's Graphs. Bradford Book (2002)
21. Sobanski, J.: Visual Math: See How Math Makes Sense. Learning Express (2002)
22. Stapleton, G., Delaney, A.: Towards overcoming deficiencies in constraint diagrams. In: IEEE Symposium on Visual Languages and Human-Centric Computing, pp. 33-40 (2007)
23. Stapleton, G., Delaney, A.: Evaluating and generalizing constraint diagrams. Visual Languages and Computing (available online) (accepted, 2008)
24. Stapleton, G., Howse, J., Taylor, J.: A decidable constraint diagram reasoning system. Journal of Logic and Computation 15(6), 975-1008 (2005)
25. Stapleton, G., Masthoff, J.: Incorporating negation into visual logics: A case study using Euler diagrams. In: Visual Languages and Computing 2007, pp. 187-194. Knowledge Systems Institute (2007)
26. Stapleton, G., Masthoff, J., Flower, J., Fish, A., Southern, J.: Automated theorem proving in Euler diagrams systems. Journal of Automated Reasoning 39, 431-470 (2007)
27. Swoboda, N., Allwein, G.: 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)
28. Winterstein, D., Bundy, A., Gurr, C.: Dr Doodle: A diagrammatic theorem prover. In: Basin, D., Rusinowitch, M. (eds.) IJCAR 2004. LNCS (LNAI), vol. 3097, pp. 331-335. Springer, Heidelberg (2004)
29. Winterstein, D., Bundy, A., Gurr, C., Jamnik, M.: An experimental comparison of diagrammatic and algebraic logics. In: International Conference on the Theory and Application of Diagrams, pp. 432-434 (2004)