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Quantitative linguistics is a large and rich field in the study of language that has brought about or played an essential role in debates such as those around Zipf’s law or the learnability of language. Using these two topics and their intersection as a case study, we identify in this thesis a fu...
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This thesis is concerned with internalizing model transformations as ‘dynamic’ modalities in modal logic. The model-theoretic operations discussed here are (strong) simulations, homomorphisms, and functional powersets. For each of these transformations, we will extend the basic modal language wit...
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We consider the modal logic ML^∞, the extension of standard modal logic where the modality ♦^∞ is added to the signature. Interpreted using Kripke semantics, the ♦^∞ modality captures the distinction between finite and infinite. We first provide a collection of results on the model theoretic aspe...
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In this thesis we investigate the proof theory of the fragment Σ_1^μ ∪ Π_1^μ of the modal mu-calculus. This fragment consists of formulas which have syntactic fixed point alternation depth of at most one. Σ_1^μ ∪ Π_1^μ contains the building blocks for interesting concepts such as common knowledge...
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In the seminal work by Awodey and Warren it was shown that the intensional identity types of Martin-Löf dependent type theory can be modelled categorically using weak factorisation systems. In this interpretation the dependent types are modelled by fibrations, i.e. the right maps of a weak factor...
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We examine modal logics employing state-based semantics. In this type of semantics, formulas are interpreted with respect to sets of possible worlds.
The logics studied extend classical modal logic with a special non-emptiness atom ne and with the inquisitive disjunction. We make use of two di...
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Rust is a systems programming language that uses a strong static type system to prevent memory safety issues (such “use-after-free” bugs and buffer overflows) that are common in programs written in languages such as C and C++. The RustBelt project (Jung et al. 2018a) has developed a machine- chec...
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We study the classical problem of representing partially ordered sets as prime spectra. A poset is said to be Priestley (resp. Esakia) representable if it is isomorphic to the prime spectrum of a bounded distributive lattice (resp. Heyting algebra). We study this problem by restricting the attent...
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We study a new model for fair division in which agents, aside from getting allocated a bundle of items (that can include both goods and chores), have also to be assigned a position on a social graph. Hence, natural fairness criteria arise that are not global, as in the classical setting, but loca...
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The seminal paper “A partition calculus in set theory” by Paul Erdös and Richard Rado is notoriously hard to read and contains many interesting results hidden behind outdated notation. This thesis therefore aims at a modernisation of the contents of the paper, in order to make the paper more acce...
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Writing a Master’s thesis is no small task, and it cannot be properly done without the help of others. As such, I would like to take this opportunity to thank everybody who helped me throughout this time, be it directly involving the thesis itself, or by simply giving me a roof over my head for t...