DS-2023-11: Cyclic Proof Systems for Modal Fixpoint Logics

DS-2023-11: 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 ill-founded proof systems for modal fixpoint logics, with and without explicit fixpoint quantifiers.

Cyclic and ill-founded proof-theory 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 ill-founded systems: a cyclic one for the weak Grzegorczyk modal logic K4Grz, based on our explanation of the phenomenon of "cyclic companionship" and ill-founded and cyclic ones for the full computation tree logic CTL* and the intuitionistic linear-time temporal logic iLTL. All systems are cut-free, and the cyclic ones for K4Grz and iLTL have fully finitary correctness conditions.

Lastly, we use a cyclic system for the modal mu-calculus to obtain a proof of the uniform interpolation property for the logic which differs from the original, automata-based one.

Item Type:	Thesis (Doctoral)
Report Nr:	DS-2023-11
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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