DS202401: Rooduijn, Jan (2024) Fragments and Frame Classes: Towards a Uniform Proof Theory for Modal Fixed Point Logics. Doctoral thesis, Universiteit van Amsterdam.
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Abstract
This thesis studies the proof theory of modal fixed point logics. In particular, we construct proof systems for various fragments of the modal mucalculus, interpreted over various classes of frames. With an emphasis on uniform constructions and general results, we aim to bring the relatively underdeveloped proof theory of modal fixed point logics closer to the wellestablished proof theory of basic modal logic. We employ two main approaches. First, we seek to generalise existing methods for basic modal logic to accommodate fragments of the modal mucalculus. We use this approach for obtaining Hilbertstyle proof systems. Secondly, we adapt existing proof systems for the modal mucalculus to various classes of frames. This approach yields proof systems which are nonwellfounded, or cyclic.
The thesis starts with an introduction and some mathematical preliminaries. In Chapter 3 we give hypersequent calculi for modal logic with the master modality, building on work by Ori Lahav. This is followed by an Intermezzo, where we present an abstract framework for cyclic proofs, in which we give sufficient conditions for establishing the bounded proof property. In Chapter 4 we generalise existing work on Hilbertstyle proof systems for PDL to the level of the continuous modal mucalculus. Chapter 5 contains a novel cyclic proof system for the alternationfree twoway modal mucalculus. Finally, in Chapter 6, we present a cyclic proof system for Guarded Kleene Algebra with Tests and take a first step towards using it to establish the completeness of an algebraic counterpart.
Item Type:  Thesis (Doctoral) 

Report Nr:  DS202401 
Series Name:  ILLC Dissertation (DS) Series 
Year:  2024 
Subjects:  Logic Mathematics 
Depositing User:  Dr Marco Vervoort 
Date Deposited:  21 Dec 2023 12:42 
Last Modified:  15 Feb 2024 17:31 
URI:  https://eprints.illc.uva.nl/id/eprint/2287 
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