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The study of the axiom of choice, AC, and of the axiom of determinacy,
AD, are often seen as complementary endeavours in set theory since
these axioms are incompatible. However, the contemporary development
of set theory has allowed the emergence of an intricate connection
between determinacy axi...
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We introduce a new topological semantics for belief logics in which the belief modality is interpreted as the closure of the interior operator. We show that our semantics validates the axioms of Stalnaker’s combined system of knowledge and belief, in fact, that it constitutes the most general ext...
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This thesis is about extracting programs from classical proofs. In the
first part, we show conservativity of Peano arithmetic over Heyting
arithmetic for Π02-sentences, an old result of Kreisel, using
Friedman’s A-translation technique. Then we present some extensions by
Parigot and Krebbers of t...
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In the present thesis we will expand Restall's completeness proof and
present it on a wider context. He proposes an adaption of the
completeness proof for constant domains predicate modal logic to the
wider case of a distributive setting expanded with unary modal
operators and enriched with const...
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Games are an important tool in mathematics and logic, providing a
clear and intuitive understanding of the notions they define or
characterize. In particular, since the seminal work of Wadge in the
1970s, game characterizations of classes of functions in Baire space
have been a rich area of resea...
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In this research, I investigate the principle of compositionality from
a formal linguistic point of view. I describe the natural language
debate surrounding the principle and argue against the usual reasons
in its favour according to systematicity, productivity and linguistic
infinity. I then dis...
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For most purposes, the information an agent can readily access is just
as important as the agent’s knowledge. This thesis explores several
approaches to reasoning about the information agents in a network can
access. The first section introduces a modality for information from
immediate connectio...
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The thesis develops a formal semantics for present necessity deontic
modals, such as should, ought to, must, and past necessity deontic
modals, such as should have, ought to have, had to. Contrary to the
traditional approaches in deontic logic, we concentrate on the
prescriptive use of such modal...
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Among the literature in belief revision, we can roughly classify it
between two main approaches. The classical approach represented in AGM
theory, based on a first order logic, suitable for static revision of
factual information. And the DEL approach, appropriate for multi-agent
learning actions ...
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Posterior Analytics I.19-22 work to connect two issues in Aristotelian
syllogistic that are not obviously connected: the (in)finitude of
predicational chains and the (in)finitude of demonstrative
processes. Chapters I.20-21 establish that in Aristotle's system, the
demonstration of a syllogistic ...