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  1.  12
    On Automating Diagrammatic Proofs of Arithmetic Arguments.Mateja Jamnik, Alan Bundy & Ian Green - 1999 - Journal of Logic, Language and Information 8 (3):297-321.
    Theorems in automated theorem proving are usually proved by formal logical proofs. However, there is a subset of problems which humans can prove by the use of geometric operations on diagrams, so called diagrammatic proofs. Insight is often more clearly perceived in these proofs than in the corresponding algebraic proofs; they capture an intuitive notion of truthfulness that humans find easy to see and understand. We are investigating and automating such diagrammatic reasoning about mathematical theorems. Concrete, rather than general diagrams (...)
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  2.  1
    What Makes an Effective Representation of Information: A Formal Account of Observational Advantages.Gem Stapleton, Mateja Jamnik & Atsushi Shimojima - 2017 - Journal of Logic, Language and Information 26 (2):143-177.
    In order to effectively communicate information, the choice of representation is important. Ideally, a chosen representation will aid readers in making desired inferences. In this paper, we develop the theory of observation: what it means for one statement to be observable from another. Using observability, we give a formal characterization of the observational advantages of one representation of information over another. By considering observational advantages, people will be able to make better informed choices of representations of information. To demonstrate the (...)
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  3.  3
    Speedith: A Reasoner for Spider Diagrams.Matej Urbas, Mateja Jamnik & Gem Stapleton - 2015 - Journal of Logic, Language and Information 24 (4):487-540.
    In this paper, we introduce Speedith which is an interactive diagrammatic theorem prover for the well-known language of spider diagrams. Speedith provides a way to input spider diagrams, transform them via the diagrammatic inference rules, and prove diagrammatic theorems. Speedith’s inference rules are sound and complete, extending previous research by including all the classical logic connectives. In addition to being a stand-alone proof system, Speedith is also designed as a program that plugs into existing general purpose theorem provers. This allows (...)
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  4.  2
    Automatic Learning of Proof Methods in Proof Planning.Mateja Jamnik, Manfred Kerber, Martin Pollet & Christoph Benzmüller - 2003 - Logic Journal of the IGPL 11 (6):647-673.
    In this paper we present an approach to automated learning within mathematical reasoning systems. In particular, the approach enables proof planning systems to automatically learn new proof methods from well-chosen examples of proofs which use a similar reasoning pattern to prove related theorems. Our approach consists of an abstract representation for methods and a machine learning technique which can learn methods using this representation formalism. We present an implementation of the approach within the ΩMEGA proof planning system, which we call (...)
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  5.  3
    On Differences Between the Real and Physical Plane.Daniel Winterstein, Alan Bundy & Mateja Jamnik - 2004 - In A. Blackwell, K. Marriott & A. Shimojima (eds.), Diagrammatic Representation and Inference. Springer. pp. 29--31.
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  6. Combined Reasoning by Automated Cooperation.Christoph Benzmüller, Volker Sorge, Mateja Jamnik & Manfred Kerber - 2008 - Journal of Applied Logic 6 (3):318-342.
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