Sökning: "Models of Type Theory"
Visar resultat 1 - 5 av 285 avhandlingar innehållade orden Models of Type Theory.
1. Cubical Intepretations of Type Theory
Sammanfattning : 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. LÄS MER
2. Localic Categories of Models and Categorical Aspects of Intuitionistic Ramified Type Theory
Sammanfattning : This thesis contains three papers, all in the general area of categorical logic, together with an introductory part with some minor results and proofs of known results which does not appear to be (easily) available in the literature.In Papers I and II we investigate the formal system Intuitionistic Ramified Type Theory (IRTT), introduced by Erik Palmgren, as an approach to predicative topos theory. LÄS MER
3. Univalent Types, Sets and Multisets : Investigations in dependent type theory
Sammanfattning : This thesis consists of four papers on type theory and a formalisation of certain results from the two first papers in the Agda language. We cover topics such as models of multisets and sets in Homotopy Type Theory, and explore ideas of using type theory as a language for databases and different ways of expressing dependencies between terms. LÄS MER
4. Aspects of Yang-Mills Theory : Solitons, Dualities and Spin Chains
Sammanfattning : One of the still big problems in the Standard Model of particle physics is the problem of confinement. Quarks or other coloured particles have never been observed in isolation. Quarks are only observed in colour neutral bound states. The strong interactions are described using a Yang-Mills theory. LÄS MER
5. Stochastic Epidemic Models : Different Aspects of Heterogeneity
Sammanfattning : This thesis is concerned with the study of stochastic epidemic models for infectious diseases in heterogeneous populations. All diseases treated are of SIR type, i.e. individuals are either Susceptible, Infectious or Recovered (and immune). LÄS MER
