DS202311: Menéndez Turata, Guillermo (2023) Cyclic Proof Systems for Modal Fixpoint Logics. Doctoral thesis, Universiteit van Amsterdam.
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Abstract
This thesis is about cyclic and illfounded proof systems for modal fixpoint logics, with and without explicit fixpoint quantifiers.
Cyclic and illfounded prooftheory allow proofs with infinite branches or paths, as long as they satisfy some correctness conditions ensuring the validity of the conclusion. In this dissertation we design a few cyclic and illfounded systems: a cyclic one for the weak Grzegorczyk modal logic K4Grz, based on our explanation of the phenomenon of "cyclic companionship" and illfounded and cyclic ones for the full computation tree logic CTL* and the intuitionistic lineartime temporal logic iLTL. All systems are cutfree, and the cyclic ones for K4Grz and iLTL have fully finitary correctness conditions.
Lastly, we use a cyclic system for the modal mucalculus to obtain a proof of the uniform interpolation property for the logic which differs from the original, automatabased one.
Item Type:  Thesis (Doctoral) 

Report Nr:  DS202311 
Series Name:  ILLC Dissertation (DS) Series 
Year:  2023 
Subjects:  Computation Logic 
Depositing User:  Dr Marco Vervoort 
Date Deposited:  30 Nov 2023 15:52 
Last Modified:  19 Feb 2024 13:35 
URI:  https://eprints.illc.uva.nl/id/eprint/2285 
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