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In this thesis we study the phenomenon of learning deductive reasoning by presenting a formal learning theory model for a class of possible proof systems which are built by misinterpretations of the rules in natural deduction system of classical logic. We will address this learning problem with a...
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Linear logic is a substructural logic that refines both classical and intuitionistic logic. In fact, linear logic is characterized by several dualities (which derive from the presence of a de Morgan negation), but at the same time has a strong constructive flavor. From a proof-theoretical perspec...
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The aim of this thesis is twofold. Firstly, to find and analyse models for non-standard natural arithmetic in a category of sheaves on a site. Secondly, to give an introduction in this area of research.
In the introduction we take the reader from the basics of category theory to sheaves and sheaf...
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This thesis proposes a new requirement that probabilistic measures of coherence should ideally satisfy. This requirement is called ‘coherence preservation’. Probabilistic measures of coherence build on the idea that coherence is the mutual support between elements of a set. Using the requirement ...
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Algorithmic randomness draws on computability theory to offer rigorous formulations of the notion of randomness for mathematical objects. In addition to having evolved into a highly technical branch of mathematical logic, algorithmic randomness prompts numerous methodological questions. This thes...
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The advantage of using Topology in formal models of knowledge and belief comes from the spatial intuitions it endorses. In the possible-worlds framework, standard topological semantics for knowledge and belief are given in terms of the interior operator, and the interpretation is unavoidably conn...
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Children learn their first language in interaction with proficient users. This
naturally exposes them to positive input, i.e. grammatically correct utterances
in context. It is still unclear however, whether they also receive negative input. That is, responses informing them about the inadequacy ...
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Current approaches to discourse coherence hypothesize a number of discourse relations which are used to link sentential units to one another. These relations, also called “coherence” or “rhetorical” relations, are defined either semantically in terms of their truth-conditional content or pragmati...
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This thesis concerns truthmaker semantics, introduced by Stephen Yablo in his book Aboutness and by Kit Fine in a series of papers. In large part, what I have accomplished here is filling in gaps. I not only fill in gaps between truthmaker semantics and related theories, I also fill in gaps withi...
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This thesis aims to render intelligible the puzzling phenomenon of double-bookkeeping in schizophrenia. Double-bookkeeping is a term that is used to capture the fact that some patients voice their delusions with unshakeable certainty, yet do not act according to the delusion. The puzzle this pose...
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We present a new scheme for quantum homomorphic encryption which is compact and allows for efficient evaluation of arbitrary polynomial-sized quantum circuits. Building on the framework of Broadbent and Jeffery and recent results in the area of instantaneous non-local quantum computation, we show...