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Valid Reasoning and Visual Representation

Dissertation, Stanford University (1991)

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  1. Topological reasoning and the logic of knowledge.Andrew Dabrowski, Lawrence S. Moss & Rohit Parikh - 1996 - Annals of Pure and Applied Logic 78 (1-3):73-110.
    We present a bimodal logic suitable for formalizing reasoning about points and sets, and also states of the world and views about them. The most natural interpretation of the logic is in subset spaces , and we obtain complete axiomatizations for the sentences which hold in these interpretations. In addition, we axiomatize the validities of the smaller class of topological spaces in a system we call topologic . We also prove decidability for these two systems. Our results on topologic relate (...)
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  • Five dogmas of logic diagrams and how to escape them.Jens Lemanski, Andrea Anna Reichenberger, Theodor Berwe, Alfred Olszok & Claudia Anger - 2022 - Language & Communication 87 (1):258-270.
    In the vein of a renewed interest in diagrammatic reasoning, this paper challenges an opposition between logic diagrams and formal languages that has traditionally been the common view in philosophy of logic and linguistics. We examine, from a philosophical point of view, what we call five dogmas of logic diagrams. These are as follows: (1) diagrams are non-linguistic; (2) diagrams are visual representations; (3) diagrams are iconic, and not symbolic; (4) diagrams are non-linear; (5) diagrams are heterogenous, and not homogenous. (...)
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