Der Begriff des ›Prototypen‹ ist der deutschsprachigen Musiktheorie nicht fremd, ohne dass jedoch seine Implikationen umfassend rezipiert worden wären. Für die Entwicklung der cognitive sciences hat die Prototypentheorie seit den 1970er Jahren eine wichtige Rolle gespielt, indem sie Prozesse der Kategorisierung untersuchte und diese ins Zentrum der Kognition stellte: »We have categories for everything we can think about. To change the concept of category itself is to change our understanding of the world.« (Lakoff) Ausgehend von einer kurzen Einführung in das Prinzip einer Kategorienbildung mit unscharfen Grenzen, nichtäquivalenten Exemplaren und flexibler Gewichtung von Merkmalen, skizziert der Beitrag das Potenzial der Prototypentheorie für die Klärung bzw. Weiterentwicklung musiktheoretischer Begriffe und schlägt Kriterien zur Beurteilung ihrer Nützlichkeit vor. / The term ›prototype‹ is not unknown in German music theory. Its implications, however, haven’t been thoroughly adopted yet. Prototype theory has played an important part in the development of cognitive sciences since the 1970s by enabling researchers to examine processes of categorization and place them in the center of cognition: »We have categories for everything we can think about. To change the concept of category itself is to change our understanding of the world.« (Lakoff) The article begins with a brief introduction into the concept of categories with vague boundaries, non-equivalent samples and adjustable emphasis of characteristics. It outlines the potential of prototype theory to clarify or further develop music theory terms. Finally, there are suggestions for criteria to evaluate their usefulness.

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The study explores the degree to which readers can use their previous linguistic knowledge, which goes beyond the immediate evidence in the input, to create mental representations of new words and how the employment of this knowledge may reduce the fuzziness of the new representations. Using self-paced reading, initial representations of novel identical forms with different grammatical functions were compared in native German speakers and advanced L2 German learners with L1 Czech. The results reveal that although both groups can employ general knowledge about German grammar when establishing new representations, the L1 native speakers outperform the L2 learners: Their new representations have more precise structure and are better differentiated from related representations with respect to their grammatical information. Modeling consequences of these findings are discussed in the context of the Ontogenesis Model of the L2 Lexical Representation and the Fuzzy Lexical Representation Hypothesis.

<p dir="ltr">Our ability to understand language and perform reasoning crucially relies on a robust system of semantic cognition (G. L. Murphy, 2002; Rogers & McClelland, 2004; Rips et al., 2012; Lake & Murphy, 2021): processes that allow us to learn, update, and produce inferences about everyday concepts (e.g., cat, chair), properties (e.g., has fur, can be sat on), categories (e.g., mammals, furniture), and relations (e.g., is-a, taller-than). Meanwhile, recent progress in the field of natural language processing (NLP) has led to the development of language models (LMs): sophisticated neural networks that are trained to predict words in context (Devlin et al., 2019; Radford et al., 2019; Brown et al., 2020), and as a result build representations that encode the knowledge present in the statistics of their training environment. These models have achieved impressive levels of performance on a range of tasks that require sophisticated semantic knowledge (e.g. question answering and natural language inference), often even reaching human parity. To what extent do LMs capture the nuances of human conceptual knowledge and reasoning? Centering around this broad question, this dissertation uses core ideas in human semantic cognition as guiding principles and lays down the groundwork to establish effective evaluation and improvement of conceptual understanding in LMs. In particular, I build on prior work that focuses on characterizing what semantic knowledge is made available in the behavior and representations of LMs, and extend it by additionally proposing tests that focus on functional consequences of acquiring basic semantic knowledge.<br><br>I primarily focus on inductive generalization (Hayes & Heit, 2018)—the unique ability of humans to rely on acquired conceptual knowledge to project or generalize novel information—as a context within which we can analyze LMs’ encoding of conceptual knowledge. I do this, since the literature surrounding inductive generalization contains a variety of empirical regularities that map to specific conceptual abstractions and shed light on how humans store, organize and use conceptual knowledge. Before explicitly analyzing LMs for these empirical regularities, I test them on two other contexts, which also feature the role of inductive generalization. First I test the extent to which LMs demonstrate typicality effects—a robust finding in human categorization literature where certain members of a category are considered to be more central to the category than are others. Specifically, I test the behavior 19 different LMs on two contexts where typicality effects modulate human behavior: 1) verification of sentences expressing taxonomic category membership, and 2) projecting novel properties from individual category members to the entire category. In both tests, LMs achieved positive but modest correlations with human typicality ratings, suggesting that they can to a non-trivial extent capture subtle differences between category members. Next, I propose a new benchmark to test the robustness of LMs in attributing properties to everyday concepts, and in making inductive leaps to endow properties to novel concepts. On testing 31 different LMs for these capacities, I find that while they can correctly attribute properties to everyday concepts and even predict the properties of novel concepts in simple settings, they struggle to do so robustly. Combined with the analyses of typicality effects, these results suggest that the ability of LMs to demonstrate impressive conceptual knowledge and reasoning behavior can be explained by their sensitivities to shallow predictive cues. When these cues are carefully controlled for, LMs show critical failures in demonstrating robust conceptual understanding. Finally, I develop a framework that can allow us to characterize the extent to which the distributed representations learned by LMs can encode principles and abstractions that characterize inductive behavior of humans. This framework operationalizes inductive generalization as the behavior of an LM after its representations have been partially exposed (via gradient-based learning) to novel conceptual information. To simulate this behavior, the framework uses LMs that are endowed with human-elicited property knowledge, by training them to evaluate the truth of sentences attributing properties to concepts. I apply this framework to test four different LMs on 13 different inductive phenomena documented for humans (Osherson et al., 1990; Heit & Rubinstein, 1994). Results from these analyses suggest that building representations from word distributions can successfully allow the encoding of many abstract principles that can guide inductive behavior in the models—principles such as sensitivity to conceptual similarity, hierarchical organization of categories, reasoning about category coverage, and sample size. At the same time, the tested models also systematically failed at demonstrating certain phenomena, showcasing their inability to demonstrate pragmatic reasoning, preference to rely on shallow statistical cues, and lack of context sensitivity with respect to high-level intuitive theories.</p>

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Pairs in involution are a Hopf algebraic structure with applications to category theory, cyclic homology and knot theory. In the present dissertation we will answer the question whether every finite-dimensional Hopf algebra admits such pairs, construct and investigate their categorical analogues, and develop, based on our previous findings, the theory of pairs in involutions for Hopf monads.

Although there is no natural internal product for hermitian forms over an algebra with involution of the first kind, we describe how tomultiply two ε-hermitian forms to obtain a quadratic form over the base field. This allows to define a commutative graded ring structure by taking together bilinear forms and ε-hermitian forms, which we call the mixedWitt ring of an algebra with involution. We also describe a less powerful version of this construction for unitary involutions, which still defines a ring, but with a grading over Z instead of the Klein group. We first describe a general framework for defining graded rings out of monoidal functors from monoidal categories with strong symmetry properties to categories of modules. We then give a description of such a strongly symmetric category Brₕ(K, ι) which encodes the usual hermitian Morita theory of algebras with involutions over a field K. We can therefore apply the general framework to Brₕ(K, ι) and theWitt group functors to define our mixed Witt rings, and derive their basic properties, including explicit formulas for products of diagonal forms in terms of involution trace forms, explicit computations for the case of quaternion algebras, and reciprocity formulas relative to scalar extensions. We intend to describe in future articles further properties of those rings, such as a λ-ring structure, and relations with theMilnor conjecture and the theory of signatures of hermitian forms.

Studien undersöker fritidshemslärares didaktiska arbete och samverkan med ämneslärare,samt rektorns roll i samverkan. Detta tema uppstod efter att vi deltagit i praktik och fåttobservera fritidshemslärarna i deras verksamhet. Tidigare forskning som används visar hurfritidshemslärare använder didaktiska arbetssätt för att planera och genomföraundervisningen. Den visar även att samverkan med ämneslärare spelar en roll i det didaktiskaarbetet på fritidsverksamheten, samt att rektorn har en betydande roll i samverkan. För attanalysera det empiriska materialet har sju begrepp använts, vilka alla har en koppling till detsociokulturella perspektivet. Det empiriska materialet består av intervjuer med fyra olikafritidshemslärare som arbetar på olika skolor. Intervjuerna spelades in och transkriberadessedan för att kunna bearbetas. Resultaten visar att fritidshemslärare planerar aktiviteter medtydliga syften, anpassar undervisningen efter elevernas behov och ser samverkan somavgörande för att uppnå detta. Trots utmaningar som tidsbrist och kommunikation, harrespondenterna en positiv syn på samverkan. De ser även rektorn som en trygghetspunkt trotseventuella brister. Resultaten och analysen jämförs därefter med den tidigare forskningen föratt ge en helhetsbild av forskningsområdet. Avslutningsvis diskuteras framtidaforskningsvägar, där en möjlig väg är att inkludera observationer i intervjuerna för att få endjupare förståelse för det didaktiska arbetet i praktiken. Därefter reflekterar vi över hur dennastudies resultat och diskussion har bidragit till professionsutveckling för lärare till fritidshem. / The study examines the didactic work of leisure-time educators and their collaboration with subject teachers, as well as the role of the principal in this collaboration. This theme emerged after our participation in practice and observation of leisure-time educators in their activities. Previous research utilized illustrates how leisure-time educators employ didactic approaches to plan and conduct teaching. It also demonstrates that collaboration with subject teachers plays a role in the didactic work of leisure-time activities, and that the principal has a significant role in this collaboration. To analyze the empirical material, seven concepts related to the sociocultural perspective have been employed. The empirical material consists of interviews with four different leisure-time educators working in different schools. The interviews were recorded and transcribed for analysis. The results indicate that leisure-time educators plan activities with clear objectives, adapt teaching to students' needs, and view collaboration as crucial for achieving this. Despite challenges such as time constraints and communication issues, respondents have a positive view of collaboration. They also perceive the principal as a point of security despite potential shortcomings. The results and analysis are then compared with previous research to provide a comprehensive overview of the research area. Finally, future research directions are discussed, with one potential avenue being the inclusion of observations in interviews to gain a deeper understanding of the didactic work in practice. Subsequently, we reflect on how the results and discussion of this study have contributed to the professional development of leisure-time educators.

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Il est acquis qu’il n’existe pas une, mais plusieurs figures de l’actionnaire. Le fait est aujourd’hui largement acté en droit : on ne compte plus les règles, dans l’ensemble des disciplines du droit des affaires, qui ne s’appliquent qu’à certaines catégories d’actionnaires plutôt qu’à tout actionnaire. Une étude d’ensemble des catégories d’actionnaires permet dès lors de déterminer, pour chacune de ces règles, quelle est la catégorie d’actionnaires « pertinente ». Une telle démarche commande en premier lieu de s’interroger sur les critères des catégories d’actionnaires. Un premier critère, suggéré en doctrine et repris en droit positif, repose sur la psychologie de l’actionnaire. Il doit être rejeté, son admission n’apparaissant juridiquement ni possible ni utile. Un second critère, qui n’a jusqu’alors pas été envisagé en tant que tel, réside dans le pouvoir de l’actionnaire. Il mérite d’être consacré, étant vecteur d’une meilleure compréhension et d’une amélioration de notre droit.L’étude des catégories d’actionnaires conduit en second lieu à les aborder individuellement au sein d’une typologie des catégories d’actionnaires. Elle permet de dégager une vision d’ensemble des pouvoirs de l’actionnaire et d’en faire apparaître toute la richesse. En confrontant les pouvoirs de l’actionnaire les uns aux autres, elle facilite en outre la recherche de leur signification et de leur bonne utilisation en droit. / The categories of shareholders. It is commonly accepted that there is not a single, but several types of shareholders. This has become a fact of law given the increasing number of rules, in every area of business law, which only apply to certain categories of shareholders rather than to all shareholders. A global study of shareholders categories will thus permit to determine, for each of these rules, which category of shareholders is the “appropriate” one. Such an approach entails first of all to raise the question of the criteria of shareholders categories. One criterion, suggested by scholars and adopted in positive law, focuses on shareholder psychology. Such criterion must be rejected, its adoption being, from a legal standpoint, neither possible nor useful. Another criterion, which until now has never been considered in its own right, is shareholder power. Such criterion should be recognized, in so far as it could both improve the law and enhance our understanding of it. The study of shareholders categories leads us next to consider them individually within a typical shareholders classification. From there, an overall picture emerges of the wide ranging possibilities of shareholders powers. Indeed, if the different powers of shareholders are compared and contrasted, it becomes easier both to define them and use them correctly legally.