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In this thesis we introduce simultaneous substitution algebras as an abstraction of simultaneous substitution operations on terms and on functions. The class of simultaneous substitution algebras is defined by a set of equations, and we prove that the equational theory generated by this set is de...
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From different angles of science, there has been a growing interest in the abilities of groups to track the truth. The Condorcet Jury Theorem (1785) states that without communication, infinitely big groups will reach a correct majority opinion with certainty. Coughlan (2000), meanwhile formulated...
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Liquid democracy is a voting system that allows citizens to vote directly, or to delegate their votes to a trusted individual. If delegations occur, the preferences of the electorate (set of voters choosing to vote directly) can exhibit different properties than the preferences of the entire soci...
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Participatory Budgeting (PB) is a process of collective decision-making in which citizens of a municipality have a direct say in the way public funds are spent. This has recently inspired a vast amount of mathematical and computational research into the way that public funds are to be allocated g...
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We initiate the study of finite characterisations and exact learnability of modal languages. A finite characterisation of a modal formula w.r.t. a class of formulas is a finite set of finite models (labelled either positive or negative) which distinguishes this formula from every other formula fr...
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How should we decide on the outcome of an election? Social choice theory offers many voting rules to answer this question, but also establishes various impossibility results showing that no single ideal rule exists. During recent years, researchers have developed a method for using axioms, i.e., ...
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The Eurovision Song Contest is the longest-running annual international music competition. In recent years, especially Italy and Sweden have obtained many successes at the song festival. Both countries select their entries through a popular national contest, respectively the Festival di Sanremo a...
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In recent years, automata theory has been brought into the realm of category theory which allowed the generalisation of results and provided new perspectives. With the introduction of the Ω-automaton, an ω-automaton which arises as a coalgebra, there is a wide range of directions to explore. Unli...
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Compilability (also known as knowledge compilation) concerns the computational complexity of preprocessing intractable problems. For some hard computational problems, under the assumption that some part of the inputs will stay fixed over time, we allow this fixed part of the instances to be prepr...
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The Bayesian Problem of Awareness Growth is Bayesianism’s apparent inability to account for the way our beliefs change in situations of awareness growth, those “a-ha, I hadn’t thought of that” moments familiar to all of us. This thesis is concerned with attempts to modify Bayesianism so as to sol...
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This thesis explores the processes an artificial agent needs to understand its environment. It extends on the Apperception Engine and intensively applies insights from Kant’s Critique of Pure Reason. Techniques from logic programming, topology, graph theory and several other disciplines are harne...