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.
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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.
Barwise, J. & Seligman, J. (1993). Imperfect Information Flow. In Proceedings of the 8th Annual IEEE symposium on Logic in Computer Science.
Barwise, J. & Seligman, J. (1997). Information Flow: The Logic of Distributed Systems. Cambridge University Press: Cambridge. Tracts in Theoretical Computer Science 44.
Barwise, J. & Shimojima, A. (1995). Surrogate Reasoning. Cognitive Studies: Bulletin of Japanese Cognitive Science Society 4(2): 7–27.
Blackburn, P. & Seligman, J. (1995). Hybrid Languages. Journal of Logic, Language, and Information 4: 251–272.
Braine, M.D.S. (1978). On the Relationship Between the Natural Logic of Reasoning and Standard Logic. Psychological Review 85: 1–21.
Clark, H.H. (1969). Linguistic Processes in Deductive Reasoning. Psychological Review 76: 387–404.
de Rijke, M. (1992). The Modal Logic of Inequality. Journal of Symbolic Logic 57(2): 566–584.
Dobson (1997). Information Enforcement and Learning: Improving Syllogistic Reasoning Skills. PhD thesis, Open University, Milton Keynes. (in preparation).
Englebretsen, G. (1992). Linear Diagrams for Syllogisms (with Relationals). Notre Dame Journal of Formal Logic 33(1): 37–69.
Gärdenfors, P. (1996). Mental Representation, Conceptual Spaces, and Metaphors. Synthese 106: 21–47.
Gargov, G. & Goranko, V. (1993). Modal Logic with Names. Journal of Philosophical Logic 22: 607–636.
Grigni, M., Papadias, D. & Papadimitriou, C. (1995). Topological Inference. In International Joint Conference on Artificial Intelligence (IJCAI '95). AAAI Press.
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).
Haarslev, V. (1995). Formal Semantics of Visual Languages using Spatial Reasoning. In IEEE symposium on Visual Languages, 156–163. IEEE Computer Society Press.
Hammer, E.M. (1995). Logic and Visual Information. Studies in Logic, Language, and Computation. CSLI Publications and FoLLI: Stanford.
Howell, R. (1976). Ordinary Pictures, Mental Representations, and Logical Forms. Synthese 33: 149–174.
Huttenlocher, J. (1968). Constructing Spatial Images: A Strategy in Reasoning. Psychological Review 75(6): 550–560.
Johnson-Laird, P. N. (1983). Mental Models. CUP.
Larkin, J. & Simon, H. (1987). Why a Diagram is (Sometimes) Worth 10,000 Words. Cognitive Science 11: 65–99.
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.
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.
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.
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.
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.
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).
Lemon, O. & Pratt, I. (1998a). On the Insufficiency of Linear Diagrams for Syllogisms. Notre Dame Journal of Formal Logic (to appear).
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).
Lemon, O., de Rijke, M. & Shimojima, A. (1999). Efficacy of Diagrammatic Reasoning (Editorial). Journal of Logic, Language, and Information 8.
Levesque, H.J. (1986). Making Believers Out of Computers. Artificial Intelligence 30: 81–108.
Levesque, H.J. (1988). Logic and the Complexity of Reasoning. Journal of Philosophical Logic 17: 355–389.
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).
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.
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.
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.
Papadimitriou, C. (1994). Computational Complexity. Addison Wesley: New York.
Pratt, I. & Schoop, D. (1998). A Complete Axiom System for Polygonal Mereotopology of the Real Plane. Journal of Philosophical Logic (to appear).
Rips, L.J. (1994). The Psychology of Proof. MIT Press: Cambridge, MA.
Schubert, L. (1976). Extending the Expressive Power of Semantic Networks. Artificial Intelligence 7(2): 163–198.
Shimojima, A. (1996). On the Efficacy of Representation. PhD thesis, Indiana University.
Shin, S.-J. (1995). The Logical Status of Diagrams. Cambridge University Press: Cambridge.
Shin, S.-J. & Lemon, O. (1999). Diagrams. Stanford Encyclopedia of Philosophy.
Sober, E. (1976). Mental Representations. Synthese 33: 101–148.
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.
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.
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.
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.
Stenning, K. & Oberlander, J. (1995). A Cognitive Theory of Graphical and Linguistic Reasoning: Logic and Implementation. Cognitive Science 19(1): 97–140.
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).
Stenning, K. and Yule, P. (1997). Image and Language in Human Reasoning: A Syllogistic llustration. Cognitive Psychology (in press).
Vallduví, E. (1992). The Informational Component. Garland: New York.
Vallduví, E. & Engdahl, E. (1997). The linguistic Realisation of Information Packaging. Linguistics (to appear).
van Benthem, J. (1984). Correspondence Theory. In Gabbay, D. & Guenthner, F. (eds.) Handbook of Philosophical Logic, volume 3. Reidel: Dordrecht.
Whitley, K.N. (1997). Visual Programming Languages: The Empirical Evidence for and Against. Journal of Visual Languages and Computing 8(1): 109–142.
Worboys, M. (1995). GIS: A Computing Perspective. Taylor and Francis: London.
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Stenning, K., Lemon, O. Aligning Logical and Psychological Perspectives on Diagrammatic Reasoning. Artificial Intelligence Review 15, 29–62 (2001). https://doi.org/10.1023/A:1006617525134
- diagrammatic reasoning
- formal semantics
- direct interpretation