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Title: Bunched logics : a uniform approach
Author: Docherty, Simon Robert
ISNI:       0000 0004 7965 0945
Awarding Body: UCL (University College London)
Current Institution: University College London (University of London)
Date of Award: 2019
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Bunched logics have found themselves to be key tools in modern computer science, in particular through the industrial-level program verification formalism Separation Logic. Despite this-and in contrast to adjacent families of logics like modal and substructural logic-there is a lack of uniform methodology in their study, leaving many evident variants uninvestigated and many open problems unresolved. In this thesis we investigate the family of bunched logics-including previously unexplored intuitionistic variants-through two uniform frameworks. The first is a system of duality theorems that relate the algebraic and Kripke-style interpretations of the logics; the second, a modular framework of tableaux calculi that are sound and complete for both the core logics themselves, as well as many classes of bunched logic model important for applications in program verification and systems modelling. In doing so we are able to resolve a number of open problems in the literature, including soundness and completeness theorems for intuitionistic variants of bunched logics, classes of Separation Logic models and layered graph models; decidability of layered graph logics; a characterisation theorem for the classes of bunched logic model definable by bunched logic formulae; and the failure of Craig interpolation for principal bunched logics. We also extend our duality theorems to the categorical structures suitable for interpreting predicate versions of the logics, in particular hyperdoctrinal structures used frequently in Separation Logic.
Supervisor: Pym, D. Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available