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    Machine-Assisted Proofs for Institutions


    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)
    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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