Reynolds, Conor (2023) Machine-Assisted Proofs for Institutions. PhD thesis, National University of Ireland Maynooth.
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Abstract
Institution theory is the abstract study of logical systems using category
theory. The theory has expanded since the ’80s to encompass and relate
a wide range of concrete logical systems. But inducting particular logical
systems into the theory can be tiresome—often straightforward, but
repetitive, technical, and prone to error. Worse, such work suffers from
the very problem which motivates abstraction: we find ourselves proving
the same things over and over again.
In this thesis we will describe a framework for easing the process
of constructing institutions and verifying their properties. The goal is
primarily to expedite the verification of those proof obligations most commonly
involved in constructing institutions. We start by encoding the
institution for first-order predicate logic, turning later to the semantics
for the Event-B modelling method. We then explore a particular logic
combination of Event-B and linear temporal logic, as well as some interesting
institution-independent constructions that enable generic logic
combinations and translations—all of which will serve as useful work in
its own right, but also as a demonstration of the framework.
Item Type: | Thesis (PhD) |
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Keywords: | Machine-Assisted; Proofs; Institutions; |
Academic Unit: | Faculty of Science and Engineering > Computer Science |
Item ID: | 19948 |
Depositing User: | IR eTheses |
Date Deposited: | 05 Jun 2025 14:26 |
URI: | https://mural.maynoothuniversity.ie/id/eprint/19948 |
Use Licence: | This item is available under a Creative Commons Attribution Non Commercial Share Alike Licence (CC BY-NC-SA). Details of this licence are available here |
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