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Liquid democracy is a collective decision-making process in which voters are allowed to delegate their vote to any peer. We consider a liquid version of judgment aggregation – a setting in which the collective decision concerns multiple interdependent issues. We translate a number of well-known n...
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This thesis considers formal approaches to accounting for the distribution of verbal mood (indicative/subjunctive) in Romance languages. Our language of focus is Italian, the most rebellious of the main Romance languages with respect to verbal mood. Italian is widely known to present a puzzle whe...
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In this document, we first develop a general framework to lift the pushout-product axioms in classical homotopy theory to the structured context of algebraic weak factorisation systems. The outcome is a notion of an algebraic monoidal model category. Within this framework, we are able to formulat...
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This thesis is a logical study of a notion of knowledge as issue-relevant information. We take issues to be the objects of inquiry. The set of issues pursued by an agent constitutes her epistemic agenda, and only the information that is relevant with respect to the issues on her agenda is process...
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This thesis is a proof-theoretic study of Contraction Free Arithmetic (CFA). We introduce CFA as a first order arithmetical theory based on a logic (GQC) which is the multiplicative fragment of LK without the structural rules of contraction. Our investigation starts by showing some basic properti...
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Extending sequent calculus with further structure or language has been a fruitful approach in structural proof theory for finding different cut-free complete proof systems. Finding translations between these different calculi not only gives new completeness results, but also insights into how the...
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In this thesis, we will develop automaton constructions as a tool for studying the equational theories of Kleene algebra with arbitrary hypotheses. Kleene algebra with hypotheses is a framework for assigning language-based semantics to Kleene algebra-based systems where extra features are formula...
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This thesis studies Esakia’s temporal Heyting calculus tHC, a temporal intuitionistic modal logic, by employing algebraic, topological, and frame-theoretic methods. First, we develop a general theory of temporal Heyting algebras, showing tHC to be sound and complete with respect to the variety an...
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In this thesis, we develop the homotopy theory of equilogical spaces and QCB (Quotients of Countably-Based) spaces. An equilogical space is a T0 countably-based space equipped with an equivalence relation, while a QCB space is the quotient of some equilogical space by its relation. We show that f...
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The gossip problem is an information distribution problem where agents try to share information between each other in the most efficient way. While an optimal order of communication is easily computed, agents often find themselves in a decentralised system and therefore rely on gossip protocols f...
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In the thesis, we extend the proof-theoretic notion of automatability to a parameterized version called fpt-automatability. Automatability gives an indication whether for a proof system automated theorem search is feasible. We develop parameterized automatability results that enrich the theory of...