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The Relationship between Aristotelian and Hasse Diagrams KU Leuven
The aim of this paper is to study the relationship between two important families of diagrams that are used in logic, viz. Aristotelian diagrams (such as the well-known ‘square of oppositions’) and Hasse diagrams. We discuss some obvious similarities and dissimilarities between both types of diagrams, and argue that they are in line with general cognitive principles of diagram design. Next, we show that a much deeper connection can be ...
Generalizing Aristotelian Relations and Diagrams KU Leuven
The square of opposition is a type of diagram that graphically represents the Aristotelian relations between sentences or formulas. It has been noted in the literature that certain extensions of the square have several Boolean subtypes. However, the traditional Aristotelian relations themselves cannot be used to distinguish these different subtypes. Furthermore, the traditional Aristotelian relations are relations between two individual ...
Logical and Geometrical Complementarities between Aristotelian Diagrams KU Leuven
This paper concerns the Aristotelian relations of contradiction, contrariety, subcontrariety and subalternation between 14 contingent formulae, which can get a 2D or 3D visual representation by means of Aristotelian diagrams. The overall 3D diagram representing these Aristotelian relations is the rhombic dodecahedron (RDH), a polyhedron consisting of 14 vertices and 12 rhombic faces (Section 2). The ultimate aim is to study the various ...
Aristotelian Diagrams for Semantic and Syntactic Consequence KU Leuven
© 2018, Springer Nature B.V. Several authors have recently studied Aristotelian diagrams for various metatheoretical notions from logic, such as tautology, satisfiability, and the Aristotelian relations themselves. However, all these metalogical Aristotelian diagrams focus on the semantic (model-theoretical) perspective on logical consequence, thus ignoring the complementary, and equally important, syntactic (proof-theoretical) perspective. In ...
Logical and Geometrical Distance in Polyhedral Aristotelian Diagrams in Knowledge Representation KU Leuven
© 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 (connections between) 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 ...
Shape Heuristics in Aristotelian Diagrams KU Leuven
Aristotelian diagrams have a long and rich history in philosophical logic. Today, they are widely used in nearly all disciplines dealing with logical reasoning. Logical geometry is concerned with the theoretical study of these diagrams, from both a logical and a visual/geometrical perspective. In this paper, we argue that the concrete shape of Aristotelian diagrams can be of great heuristic value in logical geometry. A diagram's shape can be ...