Lorenz Demey

This paper explores the interplay between logic-sensitivity and bitstring semantics in the square of opposition. Bitstring semantics is a combinatorial technique for representing the formulas that appear in a logical diagram, while logic-sensitivity entails that such a diagram may depend, not only on the formulas involved, but also on the logic with respect to which they are interpreted. These two topics have already been studied extensively in logical geometry, and are thus well-understood by themselves. However, the precise details of their interplay turn out to be far more complicated. In particular, the paper describes an elegant and natural interaction between bitstrings and logic-sensitivity, which makes perfect sense when bitstrings are viewed as purely combinatorial entities. However, when we view bitstrings as semantically meaningful entities (which is actually the standard perspective, cf. the term ‘bitstring semantics’!), this interaction does not seem to have a full and equally natural counterpart. The paper describes some attempts to address this situation, but all of them are ultimately found wanting. For now, it thus remains an open problem to capture this interaction between bitstrings and logic-sensitivity from a semantic (rather than merely a combinatorial) perspective.

This article describes the historical development of epistemic logic, focusing on the dynamic turn that has taken place in the last few decades. Although this dynamic turn was mainly motivated by technical considerations in computer science and game theory, it is argued that it can also be relevant from a more philosophical perspective: the application of dynamic epistemic logics to analyze prima facie static notions, theorems, etc. fits perfectly in a Wittgensteinian approach to philosophy as conceptual elucidation. Furthermore, it turns out that these conceptual elucidations often lead to a number of other advantages, such as a higher degree of empirical adequacy. In order to illustrate this line of argumentation, the system of public announcement logic is presented, and it is shown how this system can be used to analyze the psychological phenomenon of surprise in a conceptually and empirically fruitful way.

© 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.

© 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 of a given family of Aristotelian diagrams, and I then present and discuss a simple algorithm for automatically solving this task. This algorithm is naturally implemented within the paradigm of logic programming. In order to illustrate the theoretical fruitfulness of this algorithm, I also show how it sheds new light on several well-known families of Aristotelian diagrams.

© 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 and the nested tetrahedron. After an in-depth investigation of the geometrical properties and interrelationships of these polyhedral diagrams, we analyze the correlation between logical and geometrical distance in each of these diagrams. The outcome of this analysis is that the Aristotelian rhombic dodecahedron and tetrakis hexahedron exhibit the strongest degree of correlation between logical and geometrical distance; the tetraicosahedron performs worse; and the nested tetrahedron has the lowest degree of correlation. Finally, these results are used to shed new light on the relative strengths and weaknesses of these polyhedral Aristotelian diagrams, by appealing to the congruence principle from cognitive research on diagram design.

© 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 the square, both from an Aristotelian perspective and from a duality perspective. The results of our comparative analysis turn out to be highly nuanced.

In logical geometry, Aristotelian diagrams are studied in a precise and systematic way. Although there has recently been a good amount of progress in logical geometry, it is still unknown which underlying mathematical framework is best suited for formalizing the study of these diagrams. Hence, in this paper, the main aim is to formulate such a framework, using the powerful language of category theory. We build multiple categories, which all have Aristotelian diagrams as their objects, while having different kinds of morphisms between these diagrams. The categories developed here are assessed according to their ability to generalize previous work from logical geometry as well as their interesting category-theoretical properties. According to these evaluations, the most promising category has as its morphisms those functions on fragments that increase in informativity on both the opposition and implication relations. Focusing on this category can significantly increase the effectiveness of further research in logical geometry.

The main purpose of this paper is to reassess the debate between Boehner and Karger about Ockham’s views on the infallibility of intuitive cognition, and to present a new account of infallible intuitive cognition. After a detailed overview of Ockham’s theory of intuitive and abstractive cognition, the Boehner/Karger debate is examined. At the center of this debate are two conflicting interpretations of a certain passage in Ockham’s writings. It is shown that neither of these interpretations is ultimately successful. Next, a third interpretation is introduced and shown to be superior to the previous two. This new interpretation leads to a refutation of one of Karger’s main arguments against Boehner’s theory of the infallibility of intuitive cognition. Finally, a distinction between weak and strong infallibility is introduced, and it is argued that intuitive cognition is always weakly infallible, and often also strongly infallible.

© 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 two diagrammatic parameters are iconic/concrete versus symbolic/abstract representation and static versus dynamic representation. We briefly illustrate how different types of linguistic diagrams can be analysed in terms of the interaction between the linguistic and the diagrammatic parameters.

© 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 such as congruence/isomorphism and apprehension. The cognitive effectiveness of the different visualizations is compared for the representation of implication versus opposition relations, and for subdiagram embeddings.

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 applying the proposed measure of context-sensitivity leads to a number of precise yet highly intuitive results.