MoL-2022-26: Explorations in Coalgebraic Predicate Logic (With a Focus on Interpolation)

MoL-2022-26: Samwel, Rover Junior (2022) Explorations in Coalgebraic Predicate Logic (With a Focus on Interpolation). [Report]

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This thesis explores the area of coalgebraic predicate logic (CPL) in various ways. We describe the morphisms of CPL in great detail, motivating our choices and giving a characterisation in the form of a ‘Coalgebraic Diagram’. Furthermore, we establish an Ehrenfeucht Fraı̈ssé (EF) game for CPL, along with an adequacy result. The focus of the thesis is on interpolation results for CPL, with both a semantic and a syntactic approach. Semantically, we generalise the set up of the colimit construction in first-order logic, working towards interpolation via Robinson’s consistency. This results in an analysis that explains how colimits can only work in CPL under a tight restriction.
Syntactically, we provide an interpolation result for monotone neighbourhood frames that arise from CPL, using Maehara’s method. The proof theoretic portion of the thesis also gives a road map for further interpolation results in CPL. The latter stresses that there is yet a lot to be done in the area of CPL, both in its model theory and its proof theory. The EF-game can for example be further studied, generalised and broken down in variations. And the aforementioned restriction on colimits in CPL as well as the road map for general interpolation results can be further explored.

Item Type: Report
Report Nr: MoL-2022-26
Series Name: Master of Logic Thesis (MoL) Series
Year: 2022
Uncontrolled Keywords: Coalgebraic Predicate Logic, Predicate Liftings, Interpolation, Maehara’s method, Ehrenfeucht–Fraïssé games, Monotone Neighbourhood Functor
Subjects: Logic
Depositing User: Dr Marco Vervoort
Date Deposited: 05 Dec 2022 13:54
Last Modified: 05 Dec 2022 13:54

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