Constructions, inductive types and strong normalization

This thesis contains an investigation of Coquand's Calculus of Constructions, a basic impredicative Type Theory. We review syntactic properties of the calculus, in particular decidability of equality and type-checking, based on the equality-as-judgement presentation. We present a set-theoretic notion of model, CC-structures, and use this to give a new strong normalization proof based on a modification of the realizability interpretation. An extension of the core calculus by inductive types is investigated and we show, using the example of infinite trees, how the realizability semantics and the strong normalization argument can be extended to non-algebraic inductive types. We emphasize that our interpretation is sound for large eliminations, e.g. allows the definition of sets by recursion. Finally we apply the extended calculus to a non-trivial problem: the formalization of the strong normalization argument for Girard's System F. This formal proof has been developed and checked using the..

Parameterized monads in linguistics

A thesis submitted in partial fulfilment of the requirements of the University of Wolverhampton for the degree of Doctor of Philosophy.This dissertation follows the formal semantics approach to linguistics. It applies recent developments in computing theories to study theoretical linguistics in the area of the interaction between semantics and pragmatics and analyzes several natural language phenomena by parsing them in these theories. Specifically, this dissertation uses parameterized monads, a particular theoretical framework in category theory, as a dynamic semantic framework to reinterpret the compositional Discourse Representation Theory(cDRT), and to provide an analysis of donkey anaphora. Parameterized monads are also used in this dissertation to interpret information states as lists of presuppositions, and as dot types. Alternative interpretations for demonstratives and imperatives are produced, and the conventional implicature phenomenon in linguistics substantiated, using the framework. Interpreting donkey anaphora shows that parameterized monads is able to handle the sentential dependency. Therefore, this framework shows an expressive power equal to that of related frameworks such as the typed logical grammar and the dynamic predicate logic. Interpreting imperatives via parameterized monads also provides a compositional dynamic semantic analysis which is one of the main approaches to analysing imperatives

Beyond Logic. Proceedings of the Conference held in Cerisy-la-Salle, 22-27 May 2017

The project "Beyond Logic" is devoted to what hypothetical reasoning is all about when we go beyond the realm of "pure" logic into the world where logic is applied. As such extralogical areas we have chosen philosophy of science as an application within philosophy, informatics as an application within the formal sciences, and law as an application within the field of social interaction. The aim of the conference was to allow philosophers, logicians and computer scientists to present their work in connection with these three areas. The conference took place 22-27 May, 2017 in Cerisy-la-Salle at the Centre Culturel International de Cerisy. The proceedings collect abstracts, slides and papers of the presentations given, as well as a contribution from a speaker who was unable to attend