Artificial Intelligence Review

, Volume 15, Issue 1–2, pp 29–62 | Cite as

Aligning Logical and Psychological Perspectives on Diagrammatic Reasoning

  • Keith Stenning
  • Oliver Lemon

Abstract

We advance a theoretical framework which combines recent insights of research in logic, psychology, and formal semantics, on the nature of diagrammatic representation and reasoning. In particular, we wish to explain the varied efficacy of reasoning and representing with diagrams. In general we consider diagrammatic representations to be restricted in expressive power, and we wish to explain efficacy of reasoning with diagrams via the semantical and computational properties of such restricted `languages'. Connecting these foundational insights (from semantics and complexity theory) to the psychology of reasoning with diagrams requires us to develop the notion of the availability (to an agent) of constraints operating within representation systems, as a consequence of their direct semanticinterpretation. Thus we offer a number of fundamentaldefinitions as well as a research programme which alignscurrent efforts in the logical and psychological analysis ofdiagrammatic representation systems.

diagrammatic reasoning logic psychology efficacy formal semantics complexity constraints availability direct interpretation 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Allwein, G. & Barwise, J. (eds.) (1993). Working Papers on Diagrams and Logic, volume IULG–93–24 of Indiana University Logic Group Preprint Series. Indiana University, Visual Inference Laboratory.Google Scholar
  2. Barwise, J. & Seligman, J. (1993). Imperfect Information Flow. In Proceedings of the 8th Annual IEEE symposium on Logic in Computer Science.Google Scholar
  3. Barwise, J. & Seligman, J. (1997). Information Flow: The Logic of Distributed Systems. Cambridge University Press: Cambridge. Tracts in Theoretical Computer Science 44.Google Scholar
  4. Barwise, J. & Shimojima, A. (1995). Surrogate Reasoning. Cognitive Studies: Bulletin of Japanese Cognitive Science Society 4(2): 7–27.Google Scholar
  5. Blackburn, P. & Seligman, J. (1995). Hybrid Languages. Journal of Logic, Language, and Information 4: 251–272.Google Scholar
  6. Braine, M.D.S. (1978). On the Relationship Between the Natural Logic of Reasoning and Standard Logic. Psychological Review 85: 1–21.Google Scholar
  7. Clark, H.H. (1969). Linguistic Processes in Deductive Reasoning. Psychological Review 76: 387–404.Google Scholar
  8. de Rijke, M. (1992). The Modal Logic of Inequality. Journal of Symbolic Logic 57(2): 566–584.Google Scholar
  9. Dobson (1997). Information Enforcement and Learning: Improving Syllogistic Reasoning Skills. PhD thesis, Open University, Milton Keynes. (in preparation).Google Scholar
  10. Englebretsen, G. (1992). Linear Diagrams for Syllogisms (with Relationals). Notre Dame Journal of Formal Logic 33(1): 37–69.Google Scholar
  11. Gärdenfors, P. (1996). Mental Representation, Conceptual Spaces, and Metaphors. Synthese 106: 21–47.Google Scholar
  12. Gargov, G. & Goranko, V. (1993). Modal Logic with Names. Journal of Philosophical Logic 22: 607–636.Google Scholar
  13. Grigni, M., Papadias, D. & Papadimitriou, C. (1995). Topological Inference. In International Joint Conference on Artificial Intelligence (IJCAI '95). AAAI Press.Google Scholar
  14. Gurr, C.A. (1996). On the Isomorphism (or Otherwise) of Representations. In International Workshop on the Theory of Visual Languages (AVI'96 Post-Conference Workshop).Google Scholar
  15. Haarslev, V. (1995). Formal Semantics of Visual Languages using Spatial Reasoning. In IEEE symposium on Visual Languages, 156–163. IEEE Computer Society Press.Google Scholar
  16. Hammer, E.M. (1995). Logic and Visual Information. Studies in Logic, Language, and Computation. CSLI Publications and FoLLI: Stanford.Google Scholar
  17. Howell, R. (1976). Ordinary Pictures, Mental Representations, and Logical Forms. Synthese 33: 149–174.Google Scholar
  18. Huttenlocher, J. (1968). Constructing Spatial Images: A Strategy in Reasoning. Psychological Review 75(6): 550–560.Google Scholar
  19. Johnson-Laird, P. N. (1983). Mental Models. CUP.Google Scholar
  20. Larkin, J. & Simon, H. (1987). Why a Diagram is (Sometimes) Worth 10,000 Words. Cognitive Science 11: 65–99.Google Scholar
  21. Lemon, O. (1996). Semantical Foundations of Spatial Logics. In Aiello, L.C., Doyle, J. & Shapiro, S.C. (eds.) Principles of Knowledge Representation and Reasoning: Proceedings of the Fifth International Conference (KR '96), 212–219. Morgan Kaufmann Publishers: San Francisco, CA.Google Scholar
  22. Lemon, O. (1997a). Review of “Logic and Visual Information” by E.M. Hammer (CSLI Publications). Journal of Logic, Language, and Information 6(2): 213–216.Google Scholar
  23. Lemon, O. (1997b). Theories of Representation. In Childers, T., Kolar, P. & Svoboda, V. (eds.) Logica '96: Proceedings of the 10th International Symposium, 120–135. Filosofia Academic Publishing: Prague.Google Scholar
  24. Lemon, O. & Pratt, I. (1997a). Logical and Diagrammatic Reasoning: The Complexity of Conceptual Space. In Shafto, M. & Langley, P. (eds.) 19th Annual Conference of the Cognitive Science Society, 430–435. Lawrence Erlbaum Associates: New Jersey.Google Scholar
  25. Lemon, O. & Pratt, I. (1997b). On the Incompleteness of Modal Logics of Space: Advancing Complete Modal Logics of Place. In Kracht, M., de Rijke, M., Wansing, H. & Zakharyaschev, M. (eds.) Advances in Modal Logic, 113–130. CSLI Publications: Stanford.Google Scholar
  26. Lemon, O. & Pratt, I. (1997c). Spatial Logic and the Complexity of Diagrammatic Reasoning. Machine GRAPHICS and VISION 6(1): 89–108. (Special Issue on Diagrammatic Representation and Reasoning).Google Scholar
  27. Lemon, O. & Pratt, I. (1998a). On the Insufficiency of Linear Diagrams for Syllogisms. Notre Dame Journal of Formal Logic (to appear).Google Scholar
  28. Lemon, O. & Pratt, I. (1998b). Putting Channels on the Map: A Channel-Theoretic Semantics of Maps? In Moss, L. (ed.) Logic, Language, and Computation, Volume 2. CSLI Publications: Stanford (to appear).Google Scholar
  29. Lemon, O., de Rijke, M. & Shimojima, A. (1999). Efficacy of Diagrammatic Reasoning (Editorial). Journal of Logic, Language, and Information 8.Google Scholar
  30. Levesque, H.J. (1986). Making Believers Out of Computers. Artificial Intelligence 30: 81–108.Google Scholar
  31. Levesque, H.J. (1988). Logic and the Complexity of Reasoning. Journal of Philosophical Logic 17: 355–389.Google Scholar
  32. Nebel, B. (1995). Computational Properties of Qualitative Spatial Reasoning: First Results. In Wachsmuth, I., Rollinger, C.-R. & Brauer, W. (eds.) KI-95: Advances in Artificial Intelligence, 233–244. Springer-Verlag: Berlin. (19th German Conference on Artificial Intelligence).Google Scholar
  33. Oberlander, J., Cox, R., Tobin, R., Stenning, K. & Monaghan, P. (1996a). Individual Differences in Proof Development Strategy FollowingMultimodal Logic Teaching. In Cognitive Science Society of America. La Holla, CA.Google Scholar
  34. Oberlander, J., Stenning, K. & Cox, R. (1996b). Hyperproof: The Multi-Modal Moral. In Information Theoretic Approaches to Logic Language and Computation. Regent's College: London.Google Scholar
  35. Palmer, S.E. (1978). Fundamental Aspects of Cognitive Representation. In Rosch, E. and Lloyd, B.B. (eds.) Cognition and Categorization, 259–303. Lawrence Erlbaum Associates: Hillsdale, N.J.Google Scholar
  36. Papadimitriou, C. (1994). Computational Complexity. Addison Wesley: New York.Google Scholar
  37. Pratt, I. & Schoop, D. (1998). A Complete Axiom System for Polygonal Mereotopology of the Real Plane. Journal of Philosophical Logic (to appear).Google Scholar
  38. Rips, L.J. (1994). The Psychology of Proof. MIT Press: Cambridge, MA.Google Scholar
  39. Schubert, L. (1976). Extending the Expressive Power of Semantic Networks. Artificial Intelligence 7(2): 163–198.Google Scholar
  40. Shimojima, A. (1996). On the Efficacy of Representation. PhD thesis, Indiana University.Google Scholar
  41. Shin, S.-J. (1995). The Logical Status of Diagrams. Cambridge University Press: Cambridge.Google Scholar
  42. Shin, S.-J. & Lemon, O. (1999). Diagrams. Stanford Encyclopedia of Philosophy.Google Scholar
  43. Sober, E. (1976). Mental Representations. Synthese 33: 101–148.Google Scholar
  44. Stenning, K. (1995). Distinguishing Semantic from Processing Explanations of the Usability of Representations: Applying Expressiveness Analysis to Animation. In Lee, J. (ed.) Proceedings of Intelligent Multi-Modal Interface Workshop. AAAI Press. in press.Google Scholar
  45. Stenning, K. (1996). Embedding Logic in Communication: Lessons from the Logic Classroom. In Logic and Argumentation. Proceedings of the Colloquium on Logic and Argumentation, Royal Netherlands Academy of Arts and Sciences, 227–240. North Holland, Amsterdam.Google Scholar
  46. Stenning, K., Cox, R. & Oberlander, J. (1995). The effect of Graphical and Sentential Logic Teaching on Spontaneous External Representation. Cognitive Studies: Bulletin of the Japanese Cognitive Science Society 2(4): 56–75.Google Scholar
  47. Stenning, K. & Inder, R. (1995). Applying Semantic Concepts to Analyzing Media and Modalities. In Glasgow, J., Narayanan, N.H. & Chandrasekaran, B. (eds.) Diagrammatic Reasoning: Cognitive and Computational Perspectives. AAAI Press/TheMIT Press: Cambridge, MA.Google Scholar
  48. Stenning, K. & Oberlander, J. (1995). A Cognitive Theory of Graphical and Linguistic Reasoning: Logic and Implementation. Cognitive Science 19(1): 97–140.Google Scholar
  49. Stenning, K. & Tobin, R. (1997). Assigning Information to Modalities: Comparing Graphical Treatments of the Syllogism. In Logic, Action and Cognition: Essays in Philosophical Logic, 211–228. Kluwer (in press).Google Scholar
  50. Stenning, K. and Yule, P. (1997). Image and Language in Human Reasoning: A Syllogistic llustration. Cognitive Psychology (in press).Google Scholar
  51. Vallduví, E. (1992). The Informational Component. Garland: New York.Google Scholar
  52. Vallduví, E. & Engdahl, E. (1997). The linguistic Realisation of Information Packaging. Linguistics (to appear).Google Scholar
  53. van Benthem, J. (1984). Correspondence Theory. In Gabbay, D. & Guenthner, F. (eds.) Handbook of Philosophical Logic, volume 3. Reidel: Dordrecht.Google Scholar
  54. Whitley, K.N. (1997). Visual Programming Languages: The Empirical Evidence for and Against. Journal of Visual Languages and Computing 8(1): 109–142.Google Scholar
  55. Worboys, M. (1995). GIS: A Computing Perspective. Taylor and Francis: London.Google Scholar

Copyright information

© Kluwer Academic Publishers 2001

Authors and Affiliations

  • Keith Stenning
    • 1
  • Oliver Lemon
    • 2
  1. 1.Human Communication Research CentreEdinburgh UniversityUK
  2. 2.Center for the Study of Language and InformationStanford UniversityUSA

Personalised recommendations