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Model constructions for intuitionistic and constructive set theories, such as CZF or IZF, are commonly built upon Kripke- or Heyting-semantics for intuitionistic logic. We discuss how much of the logical structure of the underlying Kripke frame or Heyting algebra can be recovered from within the ...
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When two parties communicate they often require a certain level of security. In particular one might desire that a message cannot be altered in transit. This is called non-malleability and has been studied extensively in the non-quantum setting, but was only recently introduced in the field of qu...
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With the emergence of contemporary formal logic, it has become customary to formalise Leibniz’s Principle of the Identity of Indiscernibles (pii) by means of the following second order formula: ‘∀x∀y(∀p(p(x) ↔ p(y)) → x = y)’. Under the assumption that this formula captures the ontological meanin...
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Algorithmic complexity, also called Kolmogorov complexity and Kolmogorov-Chaitin complexity, motivates the use of techniques to approximate the complexity of objects and measure similarity between them. This thesis explores the application of these methods to patterns in textiles. A brief history...
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Recently, connections between abstract argumentation and decision making have gained increasing attention. In particular, value-based argumentation attempts to capture the specificity of deliberation concerning a choice of actions. This approach assumes that in such debates arguments appeal to ce...
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This thesis is a study of minimal mathematics, i.e., mathematics on the basis of minimal logic. We will explore different methods of working in mathematical systems that are based on minimal logic. Special emphasis will be given to finding out which results of and about intuitionistic mathematics...
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Stabilizer states are important in quantum information, computation, and error correction. Stabilizer tester is a quantum algorithm that, given an access to several copies a quantum state, tests whether the state is a stabilizer state or far from it. It was an open question whether it is possible...
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We propose a proof method that aims to show that the Fiat-Shamir proof system is SP-extractable (statement preserving) in the quantum random oracle model, if the underlying sigma-protocol has perfect unique responses. We furthermore prove that a signature scheme which is based on a Fiat-Shamir pr...
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This thesis seeks to advance the use of computational techniques for the task of philosophical interpretation. To this end I present a novel method which draws on techniques and formal tools from logic-based knowledge modeling, automated reasoning, and natural language processing to support resea...
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The fundamental problem of process-oriented qualitative models and simulations is to extract as much useful information as possible from sparse or incomplete descriptions. These qualitative reasoning approaches address the gap between the infinite complexity of the world and our partial knowledge...
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This thesis studies the ability of several compositional distributional models to recognize logical entailment relations. We first investigate the performance of recursive neural matrix and tensor networks on an artificially generated data set labelled according to a natural logic calculus. Sever...