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..

A computable expression of closure to efficient causation

International audienceIn this paper, we propose a mathematical expression of closure to efficient causation in terms of lambda-calculus; we argue that this opens up the perspective of developing principled computer simulations of systems closed to efficient causation in an appropriate programming language. An important implication of our formulation is that, by exhibiting an expression in lambda-calculus, which is a paradigmatic formalism for computability and programming, we show that there are no conceptual or principled problems in realizing a computer simulation or model of closure to efficient causation. We conclude with a brief discussion of the question whether closure to efficient causation captures all relevant properties of living systems. We suggest that it might not be the case, and that more complex definitions could indeed create crucial some obstacles to computability

Vestiges of Realism

Geschiedenis en Filosofie van Logica en Semantie

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