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- W2912432574 abstract "Van Benthem's theorem states that basic modal logicML is expressively equivalent to the bisimulation-invariantfragment of first-order logic $FO/{sim}$;we write $MLequivFO/{sim}$ for short.Hence, ML can express every bisimulation-invariant first-orderproperty and, moreover, ML can be considered an effectivesyntax for the undecidable fragment $FO/{sim}$.Over the years, many variations of this theorem have beenestablished. Rosen proved that $MLequivFO/{sim}$ is stilltrue when restricted to finite transition systems.Going beyond first-order logic, Janin and Walukiewiczshowed that the bisimulation-invariant fragment ofmonadic second-order logic MSO is precisely asexpressive as the modal $mu$-calculus~Lmu, andseveral important fragments of~Lmu have beencharacterised classically in a similar vein.However, whether $LmuequivMSO/{sim}$is true over finite transition systems,remains an open problem.This thesis is concerned with modal common knowledgelogic MLCK, another fragment of~Lmu that is moreexpressive than ML.The main result is a characterisation of MLCK overSfive structures, both classically and also in the senseof finite model theory. We achieved this result byshowing that $MLequivFO/{sim}$ over the non-elementaryclasses of (finite or arbitrary) common knowledgeKripke structures (CK Structures).The fixpoint character of the derived accessibilityrelations of CK structures poses a novel challengefor the analysis of model-theoretic games.The technical core of this thesis deals withthe development of a specific structure theoryfor specially adapted ca graphs, which we callca structures. We show thatquestions regarding CK structures can be reduced,up to bisimulation, to ca structures.Specific acyclicity properties of ca structures makeit possible to adapt and expand known locality-basedmethods, which leads to new techniques for playingfirst-order EF games over these non-elementarystructures." @default.
- W2912432574 created "2019-02-21" @default.
- W2912432574 creator A5012935978 @default.
- W2912432574 date "2018-01-01" @default.
- W2912432574 modified "2023-09-23" @default.
- W2912432574 title "Cayley Structures and the Expressiveness of Common Knowledge Logic" @default.
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- W2912432574 hasPublicationYear "2018" @default.
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