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  1.  36
    Logical Geometries and Information in the Square of Oppositions.Hans5 Smessaert & Lorenz6 Demey - 2014 - Journal of Logic, Language and Information 23 (4):527-565.
    The Aristotelian square of oppositions is a well-known diagram in logic and linguistics. In recent years, several extensions of the square have been discovered. However, these extensions have failed to become as widely known as the square. In this paper we argue that there is indeed a fundamental difference between the square and its extensions, viz., a difference in informativity. To do this, we distinguish between concrete Aristotelian diagrams and, on a more abstract level, the Aristotelian geometry. We then introduce (...)
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  2.  18
    Metalogical Decorations of Logical Diagrams.Lorenz6 Demey & Hans5 Smessaert - 2016 - Logica Universalis 10 (2-3):233-292.
    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 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 (...)
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  3.  17
    Combinatorial Bitstring Semantics for Arbitrary Logical Fragments.Lorenz6 Demey & Hans5 Smessaert - 2018 - Journal of Philosophical Logic 47 (2):325-363.
    Logical geometry systematically studies Aristotelian diagrams, such as the classical square of oppositions and its extensions. These investigations rely heavily on the use of bitstrings, which are compact combinatorial representations of formulas that allow us to quickly determine their Aristotelian relations. However, because of their general nature, bitstrings can be applied to a wide variety of topics in philosophical logic beyond those of logical geometry. Hence, the main aim of this paper is to present a systematic technique for assigning bitstrings (...)
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  4.  5
    The Interaction Between Logic and Geometry in Aristotelian Diagrams.Lorenz6 Demey & Hans5 Smessaert - 2016 - Diagrammatic Representation and Inference, Diagrams 9781:67 - 82.
    © Springer International Publishing Switzerland 2016. We develop a systematic approach for dealing with informationally equivalent Aristotelian diagrams, based on the interaction between the logical properties of the visualized information and the geometrical properties of the concrete polygon/polyhedron. To illustrate the account’s fruitfulness, we apply it to all Aristotelian families of 4-formula fragments that are closed under negation and to all Aristotelian families of 6-formula fragments that are closed under negation.
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  5.  1
    Duality Patterns in 2-PCD Fragments.Hans5 Smessaert & Lorenz6 Demey - 2017 - South American Journal of Logic 3.
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  6.  1
    The Unreasonable Effectiveness of Bitstrings in Logical Geometry.Hans5 Smessaert & Lorenz6 Demey - 2017 - In J. Y. Béziau & G. Basti (eds.), The Square of Opposition: A Cornerstone of Thought. pp. 197 - 214.
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  7.  1
    Visualising the Boolean Algebra B_4 in 3D.Hans5 Smessaert & Lorenz6 Demey - 2016 - Diagrammatic Representation and Inference, Diagrams 9781:289 - 292.
    This paper compares two 3D logical diagrams for the Boolean algebra B4, viz. the rhombic dodecahedron and the nested tetrahedron. Geometric properties such as collinearity and central symmetry are examined from a cognitive perspective, focussing on diagram design principles such as congruence/isomorphism and apprehension.
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  8.  38
    Pronounced Inferences: A Study on Inferential Conditionals.Sara9 Verbrugge, Kristien3 Dieussaert, Walter Schaeken, Hans5 Smessaert & William Van Belle - 2007 - Thinking and Reasoning 13 (2):105 – 133.
    An experimental study is reported which investigates the differences in interpretation between content conditionals (of various pragmatic types) and inferential conditionals. In a content conditional, the antecedent represents a requirement for the consequent to become true. In an inferential conditional, the antecedent functions as a premise and the consequent as the inferred conclusion from that premise. The linguistic difference between content and inferential conditionals is often neglected in reasoning experiments. This turns out to be unjustified, since we adduced evidence on (...)
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  9.  1
    Béziau’s Contributions to the Logical Geometry of Modalities and Quantifiers.Hans5 Smessaert & Lorenz6 Demey - 2015 - In Arnold Koslow & Arthur Buchsbaum (eds.), The Road to Universal Logic.
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  10.  1
    Geometric and Cognitive Differences Between Logical Diagrams for the Boolean Algebra B_4.Lorenz6 Demey & Hans5 Smessaert - 2018 - Annals of Mathematics and Artificial Intelligence 83 (2):185-208.
    © 2018, Springer International Publishing AG, part of Springer Nature. Aristotelian diagrams are used extensively in contemporary research in artificial intelligence. The present paper investigates the geometric and cognitive differences between two types of Aristotelian diagrams for the Boolean algebra B4. Within the class of 3D visualizations, the main geometric distinction is that between the cube-based diagrams and the tetrahedron-based diagrams. Geometric properties such as collinearity, central symmetry and distance are examined from a cognitive perspective, focusing on diagram design principles (...)
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