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This thesis is an investigation into the nature of logic and validity. The motivating intuition is that we could understand why the intuitionist should come to their conclusions, even if we were Platonists ourselves. According to the standard account, an argument is valid only if it preserves tru...
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This thesis explores the area of coalgebraic predicate logic (CPL) in various ways. We describe the morphisms of CPL in great detail, motivating our choices and giving a characterisation in the form of a ‘Coalgebraic Diagram’. Furthermore, we establish an Ehrenfeucht Fraı̈ssé (EF) game for CPL, a...
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We investigate the relation between arithmetic and type theory, in particular, we will consider: a constructive axiomatisation of the natural numbers known as Second-order Heyting Arithmetic (HA2), and a version of type theory known as Second-order Propositional Lambda Calculus (λP2). We give an ...
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This thesis investigates a range of fragments of FOL∞, that is, first-order logic extended with a quantifier expressing ‘there are infinitely many...’ We extend several results of Bellas Acosta [1], concerning the logic ML∞ . The logic ML∞ extends the basic modal language with an infinite modalit...
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Information is a concept that has become a point of focus in many disciplines other than information theory, but it is often unclear precisely which concept we are referring to. There are namely two main types of information. On the one hand, there is Shannon information, which is the most standa...
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This thesis researches the effect of the pragmatic “neglect-zero” tendency on indicative conditionals. Aloni (2022a) formalised this pragmatic tendency in bilateral state-based modal logic (BSML) to account for several free choice phenomena. However, this framework lacks an implication, and exten...
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Sebastian de Haro offers a new kind of scientific realism, extensional realism, which allows us to be realists, if not about the intensions of scientific terms, then at least their extensions. After examining the view and how it fits into the wider debate about scientific realism, it is argued th...
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Coinduction is the dual of induction. While inductive types are ubiquitous in functional programming languages, coinductive types, also known as codatatypes, are considerably less well-supported. Notably, Lean 4, the latest edition of an interactive theorem prover and dependently typed functional...
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Minimum Bayes risk (MBR) decoding for machine translation is getting renewed attention as it is a principled approach to neural machine translation that exhibits fewer pathologies than the widely adopted maximum a posteriori (MAP) decoding. Estimating the MBR objective, however, can be a costly e...
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Aphantasia, i.e., the inability to voluntarily form visual mental images, affects approximately 2 to 5 percent of the population and plays an important role in a more general debate revolving around the role of imagery for our cognition. This thesis investigates aphantasia by means of an interdis...
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Homotopy type theory has a model inside the category of simplicial sets which is based on Kan fibrations, but the proof of this fact can demonstrably not be made constructive. Effective Kan fibrations were introduced as an alternative to Kan fibrations in hopes of acquiring a constructive model. ...