From Analogical Proportion to Logical Proportions

International audienceGiven a 4-tuple of Boolean variables (a, b, c, d), logical proportions are modeled by a pair of equivalences relating similarity indicators ( a∧b and a¯∧b¯), or dissimilarity indicators ( a∧b¯ and a¯∧b) pertaining to the pair (a, b), to the ones associated with the pair (c, d). There are 120 semantically distinct logical proportions. One of them models the analogical proportion which corresponds to a statement of the form “a is to b as c is to d”. The paper inventories the whole set of logical proportions by dividing it into five subfamilies according to what they express, and then identifies the proportions that satisfy noticeable properties such as full identity (the pair of equivalences defining the proportion hold as true for the 4-tuple (a, a, a, a)), symmetry (if the proportion holds for (a, b, c, d), it also holds for (c, d, a, b)), or code independency (if the proportion holds for (a, b, c, d), it also holds for their negations (a¯,b¯,c¯,d¯)). It appears that only four proportions (including analogical proportion) are homogeneous in the sense that they use only one type of indicator (either similarity or dissimilarity) in their definition. Due to their specific patterns, they have a particular cognitive appeal, and as such are studied in greater details. Finally, the paper provides a discussion of the other existing works on analogical proportions

Workshop Notes of the Sixth International Workshop "What can FCA do for Artificial Intelligence?"

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The Capture of Spring: Hooke’s “Vibrative Pulse Communicated”

In 1678, Robert Hooke published a treatise on his metaphysics of vibration. Lectures de Potentia Restitutiva or Of Spring contains not only experimental and geometrical demonstrations of the spring law (which mutated into Hooke’s law after his time), but also a principle at the heart of his dynamic matter theory – Congruity and Incongruity. Namely, that harmonious and discordant forces unify, shape and separate vibrating matter. This thesis reconstructs Hooke’s production of congruity and incongruity, and the spring law, analysing the inversions, reversals and paradoxes moulding his knowledge-making practices. I argue that artificial instruments and apparatuses capable of magnifying and measuring never-before-seen minute bodies and motions also made the creation of a novel geometry necessary. I attempt to show how Hooke addressed these challenges by reassessing and reconfiguring the role of traditional Euclidean geometry, and reformulating practical-geometrical definitions to create a geometry that could demonstrate the spring law. Specifically, I focus on Hooke’s studies of vibrating bodies and vibrations, and his practical geometry. By investigating Hooke’s studies within the context of his matter theory, I show that, in an epistemological inversion, Hooke used optical instruments to shift frames of reference from the microscopic to the celestial and vice versa for his knowledge production. Further, Hooke’s work is a cohesive whole centred on his studies of the similitudes between vibrating phenomena. Finally, his knowledge-making practices are a conflation of his predominant careers as an experimentalist and geometer. By constructing natural laws from physical reality, thereby implying that nature, artificial instruments, and laws such as the spring law are related, Hooke legitimised the application of instruments and mathematics to the study of nature. This process was far from straightforward or self-evident

Design prototyping methods

textProduct development is often modeled as a cycle between phases of designing, building, and testing. This work will explore early stage build efforts of product design, which is also known as prototyping. Prototyping is a critical determinant of product success. Research shows that different approaches to prototyping can greatly affect design outcome. This work provides an integrated overview, and expansion of the existing work on design prototyping methods. Following the introduction, an extensive literature review of design prototyping tools, techniques, and methods is provided. These sources are indexed and comparatively reviewed. The capabilities of a novel hybrid prototyping technique is explored through a design case study. Next, insights from the review are integrated in a context independent prototyping strategy method. The method is developed with heuristics extracted from the literature, and additional insights from experimental studies. The technique is then experimentally evaluated. Finally, results of an extensive study of an online design repository are provided. The results include five key principles for prototype design and fabrication. The presence of these principles in the repository is validated through a novel crowd-sourced online study. The outcome effects of deploying these principles to design teams is experimentally evaluated. Overall, this research provides a guide to prototyping which includes a systematically indexed review and comparison of the existing work, as well as a novel method, and principles for design and fabrication.Mechanical Engineerin

On Musical Self-Similarity : Intersemiosis as Synecdoche and Analogy

Self-similarity, a concept borrowed from mathematics, is gradually becoming a keyword in musicology. Although a polysemic term, self-similarity often refers to the multi-scalar feature repetition in a set of relationships, and it is commonly valued as an indication for musical ‘coherence’ and ‘consistency’. In this study, Gabriel Pareyon presents a theory of musical meaning formation in the context of intersemiosis, that is, the translation of meaning from one cognitive domain to another cognitive domain (e.g. from mathematics to music, or to speech or graphic forms). From this perspective, the degree of coherence of a musical system relies on a synecdochic intersemiosis: a system of related signs within other comparable and correlated systems. The author analyzes the modalities of such correlations, exploring their general and particular traits, and their operational bounds. Accordingly, the notion of analogy is used as a rich concept through its two definitions quoted by the Classical literature—proportion and paradigm, enormously valuable in establishing measurement, likeness and affinity criteria. At the same time, original arguments by Benoît B. Mandelbrot (1924–2010) are revised, alongside a systematic critique of the literature on the subject. In fact, connecting Charles S. Peirce’s ‘synechism’ with Mandelbrot’s ‘fractality’ is one of the main developments of the present study

Models, Simulations, and the Reduction of Complexity

Modern science is a model-building activity. But how are models contructed? How are they related to theories and data? How do they explain complex scientific phenomena, and which role do computer simulations play? To address these questions which are highly relevant to scientists as well as to philosophers of science, 8 leading natural, engineering and social scientists reflect upon their modeling work, and 8 philosophers provide a commentary

Keys to Play: Music as a Ludic Medium from Apollo to Nintendo

How do keyboards make music playable? Drawing on theories of media, systems, and cultural techniques, Keys to Play spans Greek myth and contemporary Japanese digital games to chart a genealogy of musical play and its animation via improvisation, performance, and recreation. As a paradigmatic digital interface, the keyboard forms a field of play on which the book’s diverse objects of inquiry—from clavichords to PCs and eighteenth-century musical dice games to the latest rhythm-action titles—enter into analogical relations. Remapping the keyboard’s topography by way of Mozart and Super Mario, who head an expansive cast of historical and virtual actors, Keys to Play invites readers to unlock ludic dimensions of music that are at once old and new

Models, Simulations, and the Reduction of Complexity

Modern science is a model-building activity. But how are models contructed? How are they related to theories and data? How do they explain complex scientific phenomena, and which role do computer simulations play? To address these questions which are highly relevant to scientists as well as to philosophers of science, 8 leading natural, engineering and social scientists reflect upon their modeling work, and 8 philosophers provide a commentary