Abstract
Euler diagrams have been used for centuries as a means for conveying logical statements in a simple, intuitive way. They form the basis of many diagrammatic notations used to represent set-theoretic relationships in a wide range of contexts including software modelling, logical reasoning systems, statistical data representation, database search queries and file system management. In this paper we consider some notations based on Euler diagrams, in particular Spider Diagrams and Constraint Diagrams, with particular emphasis on the development of reasoning systems.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Choudhury, L., Chakraborty, M.K.: On Extending Venn Diagrams by Augmenting Names of Individuals. In: Blackwell, A.F., Marriott, K., Shimojima, A. (eds.) Diagrams 2004. LNCS (LNAI), vol. 2980, pp. 142–146. Springer, Heidelberg (2004)
Chow, S., Ruskey, F.: Drawing Area Proportional Venn and Euler Diagrams. In: Liotta, G. (ed.) GD 2003. LNCS, vol. 2912, pp. 466–477. Springer, Heidelberg (2004)
Chow, S., Ruskey, F.: Towards a General Solution to Drawing Area-Proportional Euler Diagrams. In: Proceedings of Euler Diagrams 2004. Electronic Notes in Theoretical Computer Science, vol. 134, pp. 3–18 (2005)
Clark, R.P.: Failure mode modular de-composition using spider diagrams. In: Proceedings of Euler Diagrams 2004. Electronic Notes in Theoretical Computer Science, vol. 134, pp. 19–31 (2005)
Erra, U., De Chiara, R., Scarano, V.: Vennfs: A venn diagram file manager. In: Proceedings of Information Visualisation, pp. 120–126. IEEE Computer Society, Los Alamitos (2003)
Erra, U., De Chiara, R., Scarano, V.: A system for virtual directories using euler diagrams. In: Proceedings of Euler Diagrams 2004. Electronic Notes in Theoretical Computer Science, vol. 134, pp. 33–53 (2005)
Euler, L.: Lettres a une princesse dallemagne sur divers sujets de physique et de philosophie. Letters 2, 102–108 (1775) (Berne, Socit Typographique)
Fish, A., Flower, J.: Investigating reasoning with constraint diagrams. In: Visual Language and Formal Methods, Rome, Italy. ENTCS, vol. 127, pp. 53–69. Elsevier, Amsterdam (2004)
Fish, A., Flower, J., Howse, J.: A reading algorithm for constraint diagrams. In: IEEE Symposium on Human Centric Computing Languages and Environments, Auckland, New Zealand, pp. 161–168. IEEE, Los Alamitos (2003)
Fish, A., Flower, J., Howse, J.: The semantics of augmented constraint diagrams. Journal of Visual Languages and Computing 16, 541–573 (2005)
Fish, A., Howse, J.: Computing reading trees for constraint diagrams. In: Pfaltz, J.L., Nagl, M., Böhlen, B. (eds.) AGTIVE 2003. LNCS, vol. 3062, pp. 260–274. Springer, Heidelberg (2004)
Fish, A., Howse, J.: Towards a default reading for constraint diagrams. In: Blackwell, A.F., Marriott, K., Shimojima, A. (eds.) Diagrams 2004. LNCS (LNAI), vol. 2980, pp. 51–65. Springer, Heidelberg (2004)
Fish, A., Masthoff, J.: An Experimental Study into the Default Reading of Constraint Diagrams. Visual Languages and Human Centric Computing, 287–289 (2005)
Flower, J., Howse, J.: Generating Euler diagrams. In: Hegarty, M., Meyer, B., Narayanan, N.H. (eds.) Diagrams 2002. LNCS (LNAI), vol. 2317, pp. 61–75. Springer, Heidelberg (2002)
Flower, J., Howse, J., Taylor, J.: Nesting in Euler diagrams: syntax, semantics and construction. Software and Systems Modelling 3, 55–67 (2004)
Flower, J., Masthoff, J., Stapleton, G.: Generating proofs with spider diagrams using heuristics. In: Proceedings of Distributed Multimedia Systems, International Workshop on Visual Languages and Computing, pp. 279–285. Knowledge Systems Institute (2004)
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)
Flower, J., Rodgers, P., Mutton, P.: Layout metrics for Euler diagrams. In: 7th International Conference on Information Visualisation, pp. 272–280. IEEE Computer Society Press, Los Alamitos (2003)
Flower, J., Stapleton, G.: Automated theorem proving with spider diagrams. In: Proceedings of Computing: The Australasian Theory Symposium (CATS 2004), Dunedin, New Zealand. ENTCS, vol. 91, pp. 116–132. Science Direct (January 2004)
Gil, J., Howse, J., Kent, S.: Constraint Diagrams: a step beyond UML. In: Proc. TOOLS USA 1999, pp. 453–463. IEEE Computer Society Press, Los Alamitos (1999)
Gil, J., Howse, J., Kent, S.: Formalising spider diagrams. In: Proceedings of IEEE Symposium on Visual Languages (VL 1999), Tokyo, pp. 130–137. IEEE Computer Society Press, Los Alamitos (1999)
Gil, J., Howse, J., Kent, S.: Towards a Formalization of Constraint Diagrams. In: Proc. IEEE Symposia on Human-Centric Computing (HCC 2001), Stresa, Italy, pp. 72–79. IEEE Press, Los Alamitos (2001)
Gil, J., Sorkin, Y.: The constraint diagrams editor, www.cs.technion.ac.il/Labs/ssdl/research/cdeditor/
Hammer, E.M.: Logic and Visual Information. CSLI Publications (1995)
Hayes, P., Eskridge, T., Saavedra, R., Reichherzer, T., Mehrotra, M., Bobrovnikoff, D.: Collaborative Knowledge Capture in Ontologies. In: Proceedings of the 3rd International Conference on Knowledge Capture, pp. 99–106 (2005)
Howse, J., Molina, F., Taylor, J.A.: Sound and complete diagrammatic reasoning system. In: Proc. Artificial Intelligence and Soft Computing (ASC 2000), pp. 402–408. IASTED/ACTA Press (2000)
Howse, J., Molina, F., Taylor, J.: SD2: A sound and complete diagrammatic reasoning system. In: Proc. IEEE Symp on Visual Languages (VL 2000), pp. 127–136. IEEE Press, Los Alamitos (2000)
Howse, J., Molina, F., Shin, S.-J., Taylor, J.: On diagram tokens and types. In: Hegarty, M., Meyer, B., Narayanan, N.H. (eds.) Diagrams 2002. LNCS (LNAI), vol. 2317, pp. 146–160. Springer, Heidelberg (2002)
Howse, J., Molina, F., Taylor, J.: On the completeness and expressiveness of spider diagram systems. In: Anderson, M., Cheng, P., Haarslev, V. (eds.) Diagrams 2000. LNCS (LNAI), vol. 1889, pp. 26–41. Springer, Heidelberg (2000)
Howse, J., Molina, F., Taylor, J., Kent, S.: Reasoning with spider diagrams. In: Proceedings of IEEE Symposium on Visual Languages (VL 1999), Tokyo, pp. 138–147. IEEE Computer Society Press, Los Alamitos (1999)
Howse, J., Molina, F., Taylor, J., Kent, S., Gil, J.: Spider diagrams: A diagrammatic reasoning system. Journal of Visual Languages and Computing 12(3), 299–324 (2001)
Howse, J., Schuman, S.: Precise visual modelling. Journal of Software and Systems Modeling 4, 310–325 (2005)
Howse, J., Stapleton, G., Taylor, J.: Spider diagrams. LMS J. Computation and Mathematics 8, 145–194 (2005)
Kent, S.: Constraint diagrams: Visualizing invariants in object oriented modelling. In: Proceedings of OOPSLA 1997, pp. 327–341. ACM Press, New York (1997)
Kestler, H., Müller, A., Gress, T.M., Buchholz, M.: Generalized Venn diagrams: a new method of visualizing complex genetic set relations. Bioinformatics 21(8), 1592–1595 (2005)
Kuratowski, K.: Sur le probleme des courbes gauches en topologie. Fundamenta Mathematicae 15, 271–283 (1930)
Lemon, O.: Comparing the efficacy of visual languages. In: Barker-Plummer, D., Beaver, D.I., van Benthem, J., Scotto di Luzio, P. (eds.) Words, Proofs and Diagrams, pp. 47–69. CSLI Publications (2002)
Lemon, O., Pratt, I.: Spatial logic and the complexity of diagrammatic reasoning. Machine GRAPHICS and VISION 6(1), 89–108 (1997)
More, T.: On the construction of Venn diagrams. J. Symb. Logic 24, 303–304 (1959)
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)
OMG. UML 2.0 Specification (2004), http://www.omg.org
Patrascoiu, O., Thompson, S., Rodgers, P.: Tableaux for diagrammatic reasoning. In: Proceedings of the Eleventh International Conference on Distributed Multimedia Systems. International Workshop on Visual Languages and Computing, pp. 279–286. Knowledge Systems Institute (September 2005)
Peirce, C.: Collected Papers, vol. 4. Harvard University Press (1933)
Reasoning with Diagrams Project Website (2008), http://www.cs.kent.ac.uk/projects/rwd/
Rector, A.: Specifying Values in OWL: Value Partitions and Value Sets, W3C Editors Draft 02 (2005)
Rodgers, P., Mutton, P., Flower, J.: Dynamic Euler diagram drawing. In: Visual Languages and Human Centric Computing, Rome, Italy, pp. 147–156. IEEE Computer Society Press, Los Alamitos (2004)
Ruskey, F.: A Survey of Venn Diagrams. The Electronic Journal of Combinatorics 4 (1997) (update 2001)
Schuman, S.A., Pitt, D.H.: Object-oriented subsystem specification. In: Meertens, L.G.L.T. (ed.) Program Specification and Transformation. Proc. IFIP Working Conference, pp. 313–341. North–Holland (1987)
Schuman, S.A., Pitt, D.H., Byers, P.J.: Object-oriented process specification. In: Rattray (ed.) Specification and Verification of Concurrent Systems. Proc. BCS FACS Workshop, pp. 21–70. Springer, Heidelberg (1990)
Scotto di Luzio, P.: Patching up a logic of Venn diagrams. In: Proceedings 6th CSLI Workshop on Logic, Language and Computation. CSLI Publications (2000)
Shin, S.-J.: The Logical Status of Diagrams. Cambridge University Press, Cambridge (1994)
Stapleton, G.: A survey of reasoning systems based on Euler diagrams. In: Proceedings of Euler Diagrams 2004, Brighton, UK. ENTCS, pp. 127–151 (2004)
Stapleton, G., Howse, J., Taylor, J.: A constraint diagram reasoning system. In: Proceedings of International Conference on Visual Languages and Computing, pp. 263–270. Knowledge Systems Insitute (2003)
Stapleton, G., Howse, J., Taylor, J.: A decidable constraint diagram reasoning system. Journal of Logic and Computation (to appear, 2005)
Stapleton, G., Howse, J., Taylor, J., Thompson, S.: What can spider diagrams say? In: Blackwell, A.F., Marriott, K., Shimojima, A. (eds.) Diagrams 2004. LNCS (LNAI), vol. 2980, pp. 112–127. Springer, Heidelberg (2004)
Stapleton, G., Masthoff, J., Flower, J., Fish, A., Southern, J.: Automated Theorem Proving in Euler Diagram Systems. Journal of Automated Reasoning (to appear, 2007) (accepted)
Stapleton, G., Thompson, S., Howse, J., Taylor, J.: The Expressiveness of Spider Diagrams Augmented with Constants. Journal of Visual Languages and Computing (to appear, 2008)
Stapleton, G., Thompson, S., Fish, A., Howse, J., Taylor, J.: A new language for the visualization of logic and reasoning. In: International Workshop on Visual Languages and Computing, pp. 263–270. Knowledge Systems Insitute (2005)
Stapleton, G., Thompson, S., Howse, J., Taylor, J.: The expressiveness of spider diagrams. Journal of Logic and Computation 14(6), 857–880 (2004)
Swoboda, N.: Implementing Euler/Venn Reasoning Systems. In: Anderson, M., Meyer, B., Olivier, P. (eds.) Diagrammatic Representation and Reasoning, pp. 371–386. Springer, Heidelberg (2001)
Swoboda, N., Allwein, G.: Using DAG transformations to Verify Euler/Venn Homogeneous and Euler/Venn FOL Heterogeneous Rules of Interence. In: Proceedings of GT-VMT. ENTCS. Elsevier, Amsterdam (2002)
Swoboda, N., Allwein, G.: Modeling Heterogeneous Systems. In: Hegarty, M., Meyer, B., Narayanan, N.H. (eds.) Diagrams 2002. LNCS (LNAI), vol. 2317, pp. 131–145. Springer, Heidelberg (2002)
Swoboda, N., Barwise, J.: The information content of Euler/Venn diagrams. In: Proceedings LICS workshop on Logic and Diagrammatic Information (1998)
Visual Modelling Group, http://www.cmis.bton.ac.uk/research/vmg
Venn, J.: On the diagrammatic and mechanical representation of propositions and reasonings. The London, Edinburgh and Dublin Philosophical Magazine and Journal of Science 9, 1–18 (1880)
Verroust, A., Viaud, M.: Ensuring the Drawability of Extended Euler Diagrams for up to 8 Sets. In: Blackwell, A.F., Marriott, K., Shimojima, A. (eds.) Diagrams 2004. LNCS (LNAI), vol. 2980, pp. 128–141. Springer, Heidelberg (2004)
Warmer, J., Kleppe, A.: The Object Constraint Language: Precise Modeling with UML. Addison-Wesley, Reading (1999)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Howse, J. (2008). Diagrammatic Reasoning Systems. In: Eklund, P., Haemmerlé, O. (eds) Conceptual Structures: Knowledge Visualization and Reasoning. ICCS 2008. Lecture Notes in Computer Science(), vol 5113. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-70596-3_1
Download citation
DOI: https://doi.org/10.1007/978-3-540-70596-3_1
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-70595-6
Online ISBN: 978-3-540-70596-3
eBook Packages: Computer ScienceComputer Science (R0)