-
In this thesis we introduce the notion of majorizability types, and the category MMAsm of majorizability modified assemblies. The MMAsm has the vdBB model as the interpretation of finite types. The internal logic of MMAsm captures certain version of modified realizability. Besides, both the Speci...
-
The Gibbard-Satterthwaite Theorem states that any non-dictatorial and surjective social choice function is susceptible to manipulation if there are at least three alternatives. This classical result assumes that manipulators are naive: they think that every other voter will cast a sincere ballot....
-
We study probabilistic neural language models that are obtained by marginalizing a structured latent variable in the recurrent neural network grammar (RNNG), a joint model of sentences and their syntactic structure. Supervised RNNGs produce competitive language models that are sensitive to syntac...
-
Exception handling is a widespread method of making programs fault-tolerant. Exploiting a Curry-Howard correspondence with linear logic, Caires and Pérez have shown how to use modalities denoting non-deterministically available behaviour in the π-calculus to interpret a functional programming lan...
-
This works aims to address the significance of Tennenbaum’s Theorem for the philosophy of model theory, from the perspective of non-classical inconsistent models of arithmetic. Several authors have recently argued that Tennenbaum’s Theorem, when coupled with the claim that intended addition is co...
-
This thesis develops a novel approach to a problem in the philosophy of mathematics, namely the problem of how to model the constantly evolving universe of mathematical objects. In the foundations of mathematics as formulated by set theory, this problem manifests itself as the question why the un...
-
The present thesis explores Kant’s transcendental philosophy, focusing on the cognitive processes that bring to the formation of the concept of space. In light of the interpretation proposed by Pinosio and van Lambalgen, we provide an in-depth analysis of the fundamental passages of the Critique ...
-
In this thesis we study the phenomenon of vagueness using multi-valued logics. First, we develop a collection of logics based on strong and weak Kleene truth-tables. All these logics are tolerant, they can express a change in degree for some property which is too small to be perceived as signific...
-
This thesis explores a newly-defined polyhedral semantics for intuitionistic and modal logics. Formulas are interpreted inside the Heyting algebra of open subpolyhedra of a polyhedron, and the modal algebra of arbitrary subpolyhedra with the topological interior operator. This semantics enjoys a ...
-
In this work we describe a variety of formal theories that try to capture some of our pre-theoretical notions of collection, while being careful not to fall prey to paradox. We also present some considerations that a satisfactory theory of collections must take into account, focusing in self-inst...
-
Motivated by the danger of polarization and echo chambers in social networks, we develop several logics to analyze the social phenomena balance, triadic closure and homophily. We first expand on a logical framework known from the literature with several intentions in mind. To explore measures of ...