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Data structures serve as fundamental building blocks in classical computing, allowing for efficient ways of organising, storing and manipulating data. To develop certain time-efficient quantum algorithms, classical data structures must be translated to the quantum context. However, several challe...
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In recent years, breakthroughs in model architecture and training, large availability of data, and increased computing power, conjunctively allowed AI models not only to improve performance on previous research tasks, but also to be useful in everyday life: from translation to image and text gene...
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In this thesis, we study notions of group knowledge and group belief in topological-evidential semantics. We define a multi-agent extension of the topological evidence models defined in [Özg17]. On these models, we present the evidence-based semantics of virtual group knowledge: this extends from...
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In this thesis we will expand upon a result of Jahnke and Kartas. They obtain Ax-Kochen/Ershov (AKE) principles for perfectoid fields and their tilts. Their methods all take place in a setting with only perfect fields (in particular perfectoid fields). We extend some of their results to the deepl...
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Reinforcement learning (RL), one of the most successful methods for planning in stochastic environments, suffers from sample inefficiency, requiring extensive exploration of the environment to converge on good solutions. Additionally, most RL methods function as black boxes, limiting human interv...
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A query algorithm based on homomorphism counts is a procedure for deciding membership in a class of finite relational structures using only homomorphism count queries. A left query algorithm can ask for the number of homomorphisms from any structure to the input structure, while a right query alg...
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This thesis investigates reasoning about the applicability of legal concepts, a core element in the application of law, using a variant of propositional dependence logic. The contribution of this work is two-fold.
The first contribution is the development of a new framework. This framework is ba...
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Beginning with the study of the Liar paradox, philosophers have proposed several competing theories of truth, each built on different intuitions, and they provide distinct classifications of sentences as true, false, paradoxical, or hypodoxical. In the current literature, the two dominant approac...
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This thesis explores the relationship between theoretical equivalence and representational equivalence. It mainly contains three parts: the first part summarizes current criteria of theoretical equivalence and proves some results about their comparative strengths; the second part develops a forma...
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Curry’s paradox is a peculiar paradox for at least two reasons: it is largely left out by common definitions of paradoxicality and it challenges paraconsistent solutions to the paradoxes because it can persist in a paraconsistent system. In this thesis, we study the dynamics of this paradox by ad...
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We develop a formally verified Binary Decision Diagram library in, and for, the Lean 4 programming language and proof assistant.
Binary Decision Diagrams (BDDs) are a fundamental data structure for efficient representation and manipulation of Boolean functions. Popularized by Bryant in 1986, BDD...