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Metalogical Decorations of Logical Diagrams

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Abstract

In recent years, a number of authors have started studying Aristotelian diagrams containing metalogical notions, such as tautology, contradiction, satisfiability, contingency, strong and weak interpretations of (sub)contrariety, etc. The present paper is a contribution to this line of research, and its main aims are both to extend and to deepen our understanding of metalogical diagrams. As for extensions, we not only study several metalogical decorations of larger and less widely known Aristotelian diagrams, but also consider metalogical decorations of another type of logical diagrams, viz. duality diagrams. At a more fundamental level, we present a unifying perspective which sheds new light on the connections between new and existing metalogical diagrams, as well as between object- and metalogical diagrams. Overall, the paper studies two types of logical diagrams (viz. Aristotelian and duality diagrams) and four kinds of metalogical decorations (viz. those based on the opposition, implication, Aristotelian and duality relations).

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Authors and Affiliations

  1. Center for Logic and Analytic Philosophy, KU Leuven, Leuven, Belgium

    Lorenz Demey

  2. Department of Linguistics, KU Leuven, Leuven, Belgium

    Hans Smessaert

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  1. Lorenz Demey
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  2. Hans Smessaert
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Correspondence to Lorenz Demey.

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Parts of this paper were presented at CLMPS 15 (Helsinki). We would like to thank the audience of that talk, as well as Jean-Yves Béziau, Alessio Moretti, Frédéric Sart, Fabien Schang, Margaux Smets and three anonymous reviewers for their valuable feedback. The first author holds a postdoctoral scholarship of the Research Foundation—Flanders (FWO).

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Demey, L., Smessaert, H. Metalogical Decorations of Logical Diagrams. Log. Univers. 10, 233–292 (2016). https://doi.org/10.1007/s11787-015-0136-6

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