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  1.  21
    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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  2.  49
    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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  3.  24
    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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  4.  51
    Aristotelian Diagrams in the Debate on Future Contingents: A Methodological Reflection on Hess's Open Future Square of Opposition.Lorenz6 Demey - 2019 - Sophia 58 (3):321-329.
    In the recent debate on future contingents and the nature of the future, authors such as G. A. Boyd, W. L. Craig, and E. Hess have made use of various logical notions, such as the Aristotelian relations of contradiction and contrariety, and the ‘open future square of opposition.’ My aim in this paper is not to enter into this philosophical debate itself, but rather to highlight, at a more abstract methodological level, the important role that Aristotelian diagrams can play in (...)
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  5.  75
    Some Remarks on the Model Theory of Epistemic Plausibility Models.Lorenz6 Demey - 2011 - Journal of Applied Non-Classical Logics 21 (3-4):375-395.
    The aim of this paper is to initiate a systematic exploration of the model theory of epistemic plausibility models (EPMs). There are two subtly different definitions in the literature: one by van Benthem and one by Baltag and Smets. Because van Benthem's notion is the most general, most of the paper is dedicated to this notion. We focus on the notion of bisimulation, and show that the most natural generalization of bisimulation to van Benthem-type EPMs fails. We then introduce parametrized (...)
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  6.  46
    Contemporary Epistemic Logic and the Lockean Thesis.Lorenz6 Demey - 2013 - Foundations of Science 18 (4):599-610.
    This paper studies the Lockean thesis from the perspective of contemporary epistemic logic. The Lockean thesis states that belief can be defined as ‘sufficiently high degree of belief’. Its main problem is that it gives rise to a notion of belief which is not closed under conjunction. This problem is typical for classical epistemic logic: it is single-agent and static. I argue that from the perspective of contemporary epistemic logic, the Lockean thesis fares much better. I briefly mention that it (...)
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  7. Agreeing to Disagree in Probabilistic Dynamic Epistemic Logic.Lorenz6 Demey - 2014 - Synthese 191 (3):409-438.
    This paper studies Aumann’s agreeing to disagree theorem from the perspective of dynamic epistemic logic. This was first done by Dégremont and Roy (J Phil Log 41:735–764, 2012) in the qualitative framework of plausibility models. The current paper uses a probabilistic framework, and thus stays closer to Aumann’s original formulation. The paper first introduces enriched probabilistic Kripke frames and models, and various ways of updating them. This framework is then used to prove several agreement theorems, which are natural formalizations of (...)
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  8.  7
    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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  9.  1
    Interactively Illustrating the Context-Sensitivity of Aristotelian Diagrams.Lorenz6 Demey - 2015 - Modeling and Using Context 9405:331 - 345.
    This paper studies the logical context-sensitivity of Aristotelian diagrams. I propose a new account of measuring this type of context-sensitivity, and illustrate it by means of a small-scale example. Next, I turn toward a more large-scale case study, based on Aristotelian diagrams for the categorical statements with subject negation. On the practical side, I describe an interactive application that can help to explain and illustrate the phenomenon of context-sensitivity in this particular case study. On the theoretical side, I show that (...)
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  10.  1
    The Dynamics of Surprise.Lorenz6 Demey - 2015 - Logique Et Analyse 58 (230):251 - 277.
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  11.  2
    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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  12.  2
    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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  13.  4
    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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  14.  1
    Duality Patterns in 2-PCD Fragments.Hans5 Smessaert & Lorenz6 Demey - 2017 - South American Journal of Logic 3.
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  15.  4
    Logic and Probabilistic Update.Lorenz6 Demey & Barteld Kooi - 2014 - Johan van Benthem on Logic and Information Dynamics 5:381 - 404.
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  16.  3
    Aristotelian and Duality Relations Beyond the Square of Opposition.Lorenz6 Demey & Hans5 Smessaert - 2018 - In Peter Chapman, Gem Stapleton, Amirouche Moktefi, Sarah Perez-Kriz & Francesco Bellucci (eds.), Diagrammatic Representation and Inference.
    © Springer International Publishing AG, part of Springer Nature 2018. Nearly all squares of opposition found in the literature represent both the Aristotelian relations and the duality relations, and exhibit a very close correspondence between both types of logical relations. This paper investigates the interplay between Aristotelian and duality relations in diagrams beyond the square. In particular, we study a Buridan octagon, a Lenzen octagon, a Keynes-Johnson octagon and a Moretti octagon. Each of these octagons is a natural extension of (...)
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  17.  3
    Computing the Maximal Boolean Complexity of Families of Aristotelian Diagrams.Lorenz6 Demey - 2018 - Journal of Logic and Computation 28 (6):1323-1339.
    © The Author 2018. Published by Oxford University Press. All rights reserved. Logical geometry provides a broad framework for systematically studying the logical properties of Aristotelian diagrams. The main aim of this paper is to present and illustrate the foundations of a computational approach to logical geometry. In particular, after briefly discussing some key notions from logical geometry, I describe a logical problem concerning Aristotelian diagrams that is of considerable theoretical importance, viz. the task of finding the maximal Boolean complexity (...)
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  18.  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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  19.  1
    Logical and Geometrical Distance in Polyhedral Aristotelian Diagrams in Knowledge Representation.Lorenz6 Demey & Hans5 Smessaert - 2017 - Symmetry 9 (10).
    © 2017 by the authors. Aristotelian diagrams visualize the logical relations among a finite set of objects. These diagrams originated in philosophy, but recently, they have also been used extensively in artificial intelligence, in order to study various knowledge representation formalisms. In this paper, we develop the idea that Aristotelian diagrams can be fruitfully studied as geometrical entities. In particular, we focus on four polyhedral Aristotelian diagrams for the Boolean algebra B4, viz. the rhombic dodecahedron, the tetrakis hexahedron, the tetraicosahedron (...)
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  20.  3
    Looking for the Right Notion of Epistemic Plausibility Model.Lorenz6 Demey - 2012 - In Bart Van Kerckhoven, Thierry Libert, Geert Vanpaemel & Pierre Marage (eds.), Logic, Philosophy and History of Science in Belgium II. Proceedings of the Young Researchers Days 2010. pp. 73-78.
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  21.  2
    Ockham on the (In)Fallibility of Intuitive Cognition.Lorenz6 Demey - 2014 - Philosophiegeschichte Und Logische Analyse / Logical Analysis and History of Philosophy 17:193-209.
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  22.  22
    The Porphyrian Tree and Multiple Inheritance. A Rejoinder to Tylman on Computer Science and Philosophy.Lorenz6 Demey - 2018 - Foundations of Science 23 (1):173-180.
    Tylman has recently pointed out some striking conceptual and methodological analogies between philosophy and computer science. In this paper, I focus on one of Tylman’s most convincing cases, viz. the similarity between Plato’s theory of Ideas and the object-oriented programming paradigm, and analyze it in some more detail. In particular, I argue that the platonic doctrine of the Porphyrian tree corresponds to the fact that most object-oriented programming languages do not support multiple inheritance. This analysis further reinforces Tylman’s point regarding (...)
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  23.  1
    Towards a Typology of Diagrams in Linguistics.Hans5 Smessaert & Lorenz6 Demey - 2018 - In Peter Chapman, Gem Stapleton, Amirouche Moktefi, Sarah Perez-Kriz & Francesco Bellucci (eds.), Diagrammatic Representation and Inference.
    © Springer International Publishing AG, part of Springer Nature 2018. The aim of this paper is to lay out the foundations of a typology of diagrams in linguistics. We draw a distinction between linguistic parameters — concerning what information is being represented — and diagrammatic parameters — concerning how it is represented. The six binary linguistic parameters of the typology are: mono- versus multilingual, static versus dynamic, mono- versus multimodular, object-level versus meta-level, qualitative versus quantitative, and mono- versus interdisciplinary. The (...)
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