A study of normalisation through subatomic logic

  • Andrea Aler Tubella

Student thesis: Doctoral ThesisPhD

Abstract

We introduce subatomic logic, a new methodology where by looking inside of atoms we are able to represent a wide variety of proof systems in such a way that every rule is an instance of a single, regular, linear rule scheme. We show the generality of the subatomic approach by presenting how it can be applied to several different systems with very different expressivity.In this thesis we use subatomic logic to study two normalisation procedures: cut-elimination and decomposition. In particular, we study cut-elimination by characterising a whole class of substructural logics and giving a generalised cut-elimination procedure for them, and we study decomposition by providing generalised rewriting rules for derivations that we can then apply to decompose derivations and to eliminate cycles.
Date of Award24 May 2017
LanguageEnglish
Awarding Institution
  • University of Bath
SupervisorAlessio Guglielmi (Supervisor)

Keywords

  • proof theory
  • normalisation
  • Logic

Cite this

A study of normalisation through subatomic logic
Aler Tubella, A. (Author). 24 May 2017

Student thesis: Doctoral ThesisPhD