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We present a new coalgebraic semantics for the intuitionistic modal logic known as IK or Fischer Servi logic, providing representations both for its modal spaces and for its image-finite Kripke frames. Our work is based on a recent construction by Almeida [Alm24], which has made coalgebraic analy...
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This thesis investigates the topic of arbitrary reasoning: for example a reasoning starting with a stipulation such as “let n be any natural number”. We shall consider which construal of arbitrary terms, such as indeed ‘n’, is the most appropriate, in particular how much one can argue for a refer...
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The Adoption Problem is the claim that certain basic logical principles cannot be adopted, meaning that if one does not already infer in accordance with them then one cannot start following them by explicitly being told the principle. I argue that the Adoption Problem rests on misleading assumpti...
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In the current thesis, I aim to explore numerous logical and philosophical questions regarding higher-level plurals. I begin by proposing my own conception of higher-level plural reference, dubbed Combinatorial Reference, in a way that: (a) supports the intelligibility of higher-level plurals, (b...
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The objective of classical planning is to find a sequence of actions which leads from an initial state to a goal. Several solvers for automatically solving these planning problems exist, which either return a plan (such a sequence of actions) or state that no plan exists. In the latter case, we w...
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This thesis examines the impact of several factors affecting cultural transmission, such as transmission mode, population size, social network structure, and rate of replacement, on the emergence of a preference for compositionality. It also investigates the impact of individual learning mechanis...
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This thesis departs from the idea that, by performing speech acts, we undertake commitments to act in accordance with their content (Brandom, 1983; Geurts, 2019; Hamblin, 1971; Tuzet, 2006). Three effects that speech acts have on the discourse and its participants will be studied through this len...
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This thesis investigates the modal logics of tame topologies on the Euclidean spaces. The central tool is the theory of stratifications, for which we show that closure algebras of tame topologies are determined by the decomposition spaces of their stratifications.
These methods are applied to se...
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Gender identity is typically understood as one’s innate sense of themselves as some gender, and being trans as identifying as a gender other than one’s assigned gender at birth. I argue that a lack of explanation as to what it is to have a sense of oneself as some gender has two major shortcoming...
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Since their formal introduction in 1953 by Gale and Stewart [GS53], infinite games of length ω have been a central part of the study of the continuum. However, games of uncountable length have received limited attention partly because of the inconsistency of the axiom of determinacy (AD) with ZF,...
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In this thesis we study ill-founded proof systems from a coalgebraic perspective. We present proofs as coalgebras, where correctness is enforced solely by path conditions on infinite branches, with no requirements of tree-like structure or rootedness. We apply this framework to the Gödel-Löb prov...