Search for dissertations about: "axiom"

Showing result 1 - 5 of 17 swedish dissertations containing the word axiom.

  2. 1. Cubical Intepretations of Type Theory

    Author : Simon Huber; Göteborgs universitet; []
    Keywords : NATURVETENSKAP; NATURAL SCIENCES; Dependent Type Theory; Univalence Axiom; Models of Type Theory; Identity Types; Cubical Sets;

    Abstract : The interpretation of types in intensional Martin-Löf type theory as spaces and their equalities as paths leads to a surprising new view on the identity type: not only are higher-dimensional equalities explained as homotopies, this view also is compatible with Voevodsky's univalence axiom which explains equality for type-theoretic universes as homotopy equivalences, and formally allows to identify isomorphic structures, a principle often informally used despite its incompatibility with set theory. While this interpretation in homotopy theory as well as the univalence axiom can be justified using a model of type theory in Kan simplicial sets, this model can, however, not be used to explain univalence computationally due to its inherent use of classical logic. READ MORE

  4. 2. An exposition of the consistency and independence proofs for the axiom of choice and the continuum hypothesis in axiomatic set theory with special regard to Zermeloʹs axiom system

    Author : Jan Kristoferson; Stockholms universitet; []
    Keywords : NATURVETENSKAP; NATURAL SCIENCES;

    Abstract : .... READ MORE

  5. 3. On Constructive Sets and Partial Structures

    Author : Olov Wilander; Erik Palmgren; Viggo Stoltenberg-Hansen; Bas Spitters; Uppsala universitet; []
    Keywords : NATURVETENSKAP; NATURAL SCIENCES; Mathematical Logic; Matematisk logik;

    Abstract : The first three papers in this thesis study the formalisation of a set in type theory as a data type with an equivalence relation – an object usually known as a setoid. The corresponding formalisation of a locally small category is called an E-category. READ MORE

  6. 4. A Model of Type Theory in Cubical Sets

    Author : Simon Huber; Göteborgs universitet; []
    Keywords : NATURVETENSKAP; NATURAL SCIENCES; NATURVETENSKAP; NATURAL SCIENCES; Models of dependent type theory; cubical sets; Univalent Foundations;

    Abstract : The intensional identity type is one if the most intricate concepts of dependent type theory. The recently discovered connection between homotopy theory and type theory gives a novel perspective on the identity type. READ MORE

  7. 5. SLDFA-resolution : computing answers for negative queries

    Author : Torbjörn Näslund; Linköpings universitet; []
    Keywords : NATURVETENSKAP; NATURAL SCIENCES;

    Abstract : The notion of SLDNF-resolution gives a theoretical foundation for implementation of logic programming languages. However, a major drawback of SLDNF-resolution is that for negative queries it can not produce answers other than yes or no. Thus, only a limited class of negative queries can be handled. READ MORE