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This thesis contains a study of generalizations of first order quantification. In a sense, the quantifiers studied here stand to ∀ and ∃ as the modal operators 2 and 3 stand to the universal modality.
The idea behind separating this class of quantifiers is based on the following intuition. We ...
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This dissertation is about the design of temporal logics that deal with
changing time granularities. Time granularity can be defined as the resolution
power of the temporal qualification of a statement. Providing a formalism with
the concept of time granularity makes it possible to specify ti...
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Historically, cryptology was primarily concerned with developing "secret scripts" (cryptography) and studying their reliability (cryptanalysis). After WWII, largely influenced by Claude Shannon's information theory, cryptology became a science founded on mathematical principles. A second major br...
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This dissertation is about logic. It investigates three different ways of viewing logic—three different ways of answering the same question: How can logical principles be justified? It considers an ontological perspective in the fourth chapter, a transcendental perspective in the third chapter, a...
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In this dissertation I study abduction, that is, reasoning from an
observation to its possible explanations, from a logical point of view.
This approach naturally leads to connections with theories of explanation
in the philosophy of science, and to computationally oriented theories
of belief...
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n this dissertation, we discuss several issues in recursion theory that relate to measure and randomness. The central concept in recursion theory is the concept of a "recursive set." A set is recursive if an algorithm exists to determine whether something is an element of this set. When studying ...
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Most research reported in the thesis concerns the so-called Minimum
Description Length (MDL) Principle. The MDL Principle is a general
method for inductive inference. The fundamental idea behind the MDL
Principle is that any regularity in a given set of data can be used to
compres...