logical geometry
 
 


 
 

Introduction to Logical Geometry

  • introductory course at ESSLLI 2018: the 30th European Summer School in Logic, Language and Information, Sofia, Bulgaria, August 6 - 17, 2018

  • by Lorenz Demey & Hans Smessaert

  • abstract (on the ESSLLI website)



  • slides (available in PDF format):

    1. Basic Concepts and Bitstring Semantics (update 13/08/2018)

    2. Abstract-Logical Properties of Aristotelian Diagrams, Part I (update 14/08/2018)

    3. Visual-Geometric Properties of Aristotelian Diagrams (update 16/08/2018)

    4. Abstract-Logical Properties of Aristotelian Diagrams, Part II (update 16/08/2018)

    5. Case Studies and Philosophical Outlook



  • recommended reading:

    1. Basic Concepts and Bitstring Semantics

      • Demey, Lorenz (2018).
        'Metalogic, Metalanguage and Logical Geometry'. Logique et Analyse. 24 pp.
        => preprint available in PDF format (for the course: focus on sections 1 - 2)

      • Smessaert, Hans & Lorenz Demey (2015).
        'Béziau's Contributions to the Logical Geometry of Modalities and Quantifiers'. In: Arnold Koslow & Arthur Buchsbaum (eds.) The Road to Universal Logic. Heidelberg: Springer, 475-493.
        => preprint available in PDF format; paper available in PDF format from Springer (for the course: focus on sections 3 - 7)

      • Smessaert, Hans & Lorenz Demey (2017).
        'The Unreasonable Effectiveness of Bitstrings in Logical Geometry'. In: Jean-Yves Beziau & Gianfranco Basti (eds.) The Square of Opposition: A Cornerstone of Thought, Springer, Basel. 197-214.
        => preprint available in PDF format; paper available in PDF format from Springer

      • Demey, Lorenz & Hans Smessaert (2018).
        'Combinatorial Bitstring Semantics for Arbitrary Logical Fragments'. Journal of Philosophical Logic 47/2, 325–363.
        => preprint available in PDF format; paper available in PDF format from Springer (for the course: focus on sections 1 - 3)

    2. Abstract-Logical Properties of Aristotelian Diagrams, Part I

      • Smessaert, Hans & Lorenz Demey (2014).
        'Logical Geometries and Information in the Square of Oppositions'. Journal of Logic, Language and Information 23/4, 527-565.
        => preprint available in PDF format; paper available in PDF format from Springer

      • Demey, Lorenz & Hans Smessaert (2016).
        'Metalogical Decorations of Logical Diagrams'. Logica Universalis 10/2, 233–292.
        => preprint available in PDF format; paper available in PDF format from Springer (for the course: focus on sections 4 - 6)

      • Demey, Lorenz & Hans Smessaert (2018).
        'Aristotelian and Duality Relations Beyond the Square of Opposition', In: Peter Chapman, Gem Stapleton, Amirouche Moktefi, Sarah Perez-Kriz & Francesco Bellucci (eds.), Diagrammatic Representation and Inference. Lecture Notes in Artificial Intelligence (LNAI) 10871. Heidelberg: Springer, 640 – 656.
        => preprint available in PDF format; paper available in PDF format from Springer

      • Demey, Lorenz & Hans Smessaert (2017).
        'Duality in Logic and Language'. In: James Fieser & Bradley Dowden (eds.), Internet Encyclopedia of Philosophy. Martin, TN: University of Tennessee. 37 pp.
        => paper available online

    3. Visual-Geometric Properties of Aristotelian Diagrams

      • Demey, Lorenz & Hans Smessaert (2016).
        'The Interaction between Logic and Geometry in Aristotelian Diagrams'. In: Mateja Jamnik, Yuri Uesaka & Stephanie Elzer Schwartz (eds.) Diagrammatic Representation and Inference. Lecture Notes in Artificial Intelligence (LNAI) 9781. Springer International Publishing, 67-82.
        => preprint available in PDF format; paper available in PDF format from Springer

      • Demey, Lorenz & Hans Smessaert (2014).
        'The Relationship between Aristotelian and Hasse Diagrams'. In: Tim Dwyer, Helen Purchase & Aidan Delaney (eds.) Diagrammatic Representation and Inference. Lecture Notes in Artificial Intelligence (LNAI) 8578. Heidelberg: Springer, 213-227.
        => preprint available in PDF format; paper available in PDF format from Springer

      • Demey, Lorenz & Hans Smessaert (2017).
        'Logical and Geometrical Distance in Polyhedral Aristotelian Diagrams in Knowledge Representation'. Symmetry 9/10, 204. 22 pp.
        => paper available in PDF format (open access) from MDPI (for the course: focus on sections 3 - 4)

      • Demey, Lorenz & Hans Smessaert (2018).
        'Geometric and Cognitive Differences between Logical Diagrams for the Boolean Algebra B_4'. Annals of Mathematics and Artificial Intelligence 83/2, 185-208.
        => preprint available in PDF format; paper available in PDF format from Springer (for the course: focus on sections 3 - 7)

    4. Abstract-Logical Properties of Aristotelian Diagrams, Part II

      • Demey, Lorenz & Hans Smessaert (2018).
        'Combinatorial Bitstring Semantics for Arbitrary Logical Fragments'. Journal of Philosophical Logic 47/2, 325–363.
        => preprint available in PDF format; paper available in PDF format from Springer (for the course: focus on sections 4 - 5)

      • Demey, Lorenz (2018).
        ‘Computing the Maximal Boolean Complexity of Families of Aristotelian Diagrams’. Journal of Logic and Computation. 21 pp.
        => preprint available in PDF format; paper available in PDF format from Oxford University Press; Prolog code available in PDF format

      • Demey, Lorenz (2018).
        'Boolean Considerations on John Buridan's Octagons of Opposition'. History and Philosophy of Logic. 22 pp.
        => preprint available in PDF format

      • Demey, Lorenz (2015).
        'Interactively Illustrating the Context-Sensitivity of Aristotelian Diagrams'. In: Henning Christiansen, Isidora Stojanovic and George Papadopoulos (eds.) Modeling and Using Context. Lecture Notes in Artificial Intelligence (LNAI) 9405. Heidelberg: Springer, 331-345.
        => preprint available in PDF format; paper available in PDF format from Springer; interactive illustration available here


    5. Case Studies and Philosophical Outlook

      • Demey, Lorenz (2018).
        'The Logical Geometry of Russell's Theory of Definite Descriptions'. Submitted. 33 pp.
        => preprint available in PDF format

      • Demey, Lorenz (2018).
        'A Hexagon of Opposition for the Theism/Atheism Debate', Philosophia. 8 pp.
        => preprint available in PDF format; paper available in PDF format from Springer

      • Demey, Lorenz (2018).
        'From Euler Diagrams in Schopenhauer to Aristotelian Diagrams in Logical Geometry'. Submitted. 25 pp.
        => preprint available in PDF format


 
 

December 2, 2018   www.logicalgeometry.org