Representation Matters in Cyclic Proof Theory

Type: Licentiate thesis
Supervisors: Graham E. Leigh and Bahareh Afshari
Digital copy: Available on GUPEA

A compilation thesis, consisting of two research articles, exploring cyclic proof theory from the perspective of proof representation, and an accompanying kappa.

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An Abstract Framework for the Analysis of Cyclic Derivations

Type: Master’s thesis
Supervisor: Bahareh Afshari
Digital copy: Available on the ILLC eprints server

We propose a categorical framework characterizing the traces through the pre-proofs of cyclic proof systems. This allows many aspects of cyclic proof theory to be studied in a general manner.

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A Constructive Analysis of First-Order Completeness Theorems in Coq

Type: Bachelor’s thesis
Advisors: Dominik Kirst and Yannick Forster
Supervisor: Gert Smolka

We mechanize various completeness results for first-order logic in the interactive theorem prover Coq. The focus is on pinning down when and which non-constructive principles are needed to obtain these results.

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