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The phase transition that we will focus on is about fast growing
sequences, which were discovered by Friedman. PA can prove that the
length of these sequences remains finite, but IΣ_2 cannot. IΣ_2 is the
subsystem of PA where the induction scheme is limited to induction of
Σ_2 formulas. This syst...
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Degrees of Non-Determinacy and Game Logics on Cardinals under the
Axiom of Determinacy
Zhenhao Li
Abstract:
Blass showed that on each infinite cardinal, there is an algebra
structure of games on it. Blass defined a reducibility relation on
games via which he classified games into degrees of non...
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In this thesis we study relation liftings in the context of
coalgebraic modal logic. In the first part of the thesis we look for
conditions on relation liftings that can be used to define a notion of
bisimilarity between states in coalgebras, such that two states are
bisimilar if and only if the...
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The study of partial algebras is the part of universal algebra which
deals with structures whose operations are not defined everywhere. A
natural question to ask if faced with a partial algebra is whether or
not it can be completed, i.e. embedded into a total algebra. If
furthermore we take part...
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In this thesis the syntax and semantics of four-valued first-order
predicate logic are introduced. When we define the semantics, we use
4-cylindric set algebras. Then we define 4-cylindric algebras which
are supposed to reflect the algebraic properties of this logic. We
give a method for constru...
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It has long been argued that incorporating a notion of discontinuity
in phrase-structure is desirable, given phenomena such as
topicalization and extraposition, and particular features of languages
such as cross-serial dependencies in Dutch and the German
Mittelfeld. Up until recently this was ma...
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We develop a formal model of opinion polls in elections and study how
they influence voting behaviour, and thereby elections outcomes. We
analyse two settings. In the first, we study a voter's incentives to
misrepresent her preferences after receiving poll information. We vary
the amount of infor...
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Frege is highly valued as a logician by Russell and Wittgenstein, the
latter nonetheless concludes in his Tractatus that one of Frege's
central notions, the judgment stroke, is "logically quite
meaningless". In order to see why Wittgenstein thinks so, we will
investigate the 'indirect interpretat...
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Two-dimensional semantics is a formal framework used to characterize
the meaning of sentences and sub-sentential expressions and
distinguished by the view according to which the extension of an
expression depends on two dimensions. Contextual philosophical
interpretations of that framework intend...
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This thesis considers ontological commitments from a semantic
perspective. Quine's logic/language criterion for ontological
commitment is a starting point for a discussion of correlations
between ontological commitment and semantics. I discuss some
peculiarities of Quine's criterion for ontologic...
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Mechanism design is a field that deals with designing algorithms for
making decisions based on the preferences of the agents in such a way
that the outcome is guaranteed to be good for society and the agents
are not incentivised to misreport their preferences. An appropriate
mechanism manages to ...