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In this dissertation we study questions relevant to the foundations of
mathematics, particularly the real number continuum. We look at
regularity properties of sets of real numbers on one hand, and
definability of such sets on the other. By ``regularity properties''
we are referring to certain de...
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How can we solve computational tasks when we simply don't have enough time to
process all the data? For example, given a sequence of numbers, can we
determine if they start repeating by looking at just a few of them? Or, given
query access to some boolean function $f$, how many queries to $f$ do...
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The aim of this dissertation is two-fold. First, we wish to present an
alternative to the dominant metaphilosophical approaches that try to
answer the question of what philosophy is by providing a normative
answer, i.e. an answer based on each philosopher's views on what
philosophy (proper) shoul...
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We examine doxastically inspired variants and extensions of Dependence
Logic which arise from the consideration of announcement operators and
non-functional dependence atoms. We solve several open questions of the
area, among them the following two:
1.The \forall^1 quantifier of (Kontinen and Vää...
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Binary Aggregation with Integrity Constraints
Umberto Grandi
This dissertation presents the framework of binary aggregation with integrity constraints, positioning it with respect to existing frameworks for the study of collective decision making developed in Social Choice Theory and Artificial...
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The starting point of this dissertation is a central question in epistemology and epistemic logic, statable roughly as follows: is it a necessary condition of an agent's knowing some propositions P_1,…,P_n that she has done enough empirical investigation of the world so that she could know any lo...
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Mereology, as a form of philosophical or applied research, begins with the
assumption that objects have parts. Cars, people, planets, and galaxies are
organized part-to-whole. Indeed the entire range of concrete entities will be
conceived as having a certain decompositional makeup. The study of m...
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The goal of this dissertation is to give a logical representation of the
knowledge dynamics that takes place during communication. I present a
number of different logical frameworks for a number of different scenarios,
ranging from an email conversation where all information that is sent is
consi...
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Game design theories aim to assist game developers in creating and
understanding games. Applied theory for game design supports
creativity, speeds up the design process, and increases quality of
games. This dissertation presents two theoretical frameworks for
designing games and discusses how des...
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Words like many and few have a dual nature: though traditionally
analyzed as quantifiers (~many of the houses~), they also behave like
gradable adjectives (~few/fewer houses~). In fact, such terms pattern
syntactically and semantically with both quantifiers and
adjectives. Why aren't they confine...
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This thesis contributes to the development of Soft
Dynamic Epistemic Logic. Soft Dynamic Epistemic Logic has been introduced
to deal with a number of informational phenomena, including belief
revision. The work in this thesis extends the scope of Soft Dynamic
Epistemic Logic to belief contraction...