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A compositional theory of truth with the induction principle extended to sentences containing the truth predicate is not conservative over the base theory. It is unknown whether compositionality or extended induction contributes more to the nonconservativity result. This thesis follows Heck’s cla...
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Solomonoff’s theory of inductive inference is often regarded as a gold standard for formal theories of learning. However, several results have shown that Solomonoff’s predictor fails to converge in a greater variety of circumstances than originally thought, exemplified by Hutter’s and Muchnik’s r...
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In dependent type theory with an impredicative universe, the usual encodings for inductive types borrowed from System F do not satisfy the dependent elimination rule (equivalently, no form of the η-rule holds). Two refinements of these encodings have been proposed to remedy this. Both apply to al...
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Privacy is ever so important in the digital age. To demand protection against privacy invasions, a necessary preliminary step is to elucidate what privacy is. This thesis aims to investigate the nature of privacy via two main research directions. First, throughout this thesis, I motivate and defe...
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Visual information is commonly assumed to complement distributional semantics in achieving human-like concept understanding, motivating development and evaluation of various vision-language models (VLMs). However, there have been mixed findings on when and how VLMs outperform unimodal LMs. One ke...
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This thesis presents a comprehensive investigation into semantically underspecified user queries in Question Answering (QA) scenarios of human-machine interaction. Drawing from a wide range of theoretical insights in linguistics and existing research in Natural Language Processing (NLP), we first...
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This thesis studies logical properties in lattices of modal logics, focusing on union-splittings, the axiomatization problem, and the rule dichotomy property. We use semantic approaches to investigate these topics by working with the theory of stable canonical rules and formulas. Under the modal ...
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This thesis examines the relationship between embodiment and agency with specific reference to Artificial Intelligence (AI) models. It argues that a sense of embodiment is a necessary condition of agency because agents must be able to sense and manipulate the external world that they inhabit. I a...
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The recent success of deep-learning based Large Language Models (LLMs) (Grattafiori et al. 2024; T. Brown et al. 2020) across a wide range of tasks has established them as the most promising candidate for achieving human-level Artificial Intelligence (AI). However, their simultaneous systematic f...
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A new model for deep disagreement is derived from Presuppositional Epistemology. This is done by a critical appraisal of an attempt to unify Duncan Pritchard’s Quasi-Fideism with the Presuppositional Apologetic by Nicholas Smith. Quasi-Fideism is a version of Wittgenstein’s Hinge Epistemology. Th...
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Nested sequent calculus augments the formalism of standard Gentzen-style sequents by allowing nesting of sequents, giving them a tree-like structure. In the classical modal setting, the resulting calculus is invertible, enabling terminating root-first proof search without backtracking. While prov...