MoL-2016-21: Canonical Rules on Neighbourhood Frames

MoL-2016-21: Tuyt, Olim F. (2016) Canonical Rules on Neighbourhood Frames. [Report]

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Abstract

This thesis is a study of logics whose semantics is based on neighbourhood frames. Neighbourhood frames are a generalization of Kripke frames and are generally used as a semantic framework for non-normal modal logics. We study logics with a neighbourhood based semantics by means of canonical rules and formulas. Canonical rules and formulas have been extensively studied in the context of lattices of normal modal logics, in particular for obtaining uniform axiomatizations for these logics. In this thesis, we develop analoguous methods for lattices of logics with a neighbourhood based semantics. Firstly we define stable canonical rules for neighbourhood frames to axiomatize all classical and monotonic modal logics and multi-conclusion consequence relations. We look at two instances of these rules, namely stable rules and Jankov rules. Modal logics and multi-conclusion consequence relations axiomatized by the former have the finite model property whereas the latter axiomatizes splittings in the lattice CExtSE of all classical modal multi-conclusion consequence relations. Secondly we look at Instantial Neighbourhood Logic. We define co-stable canonical rules to axiomatize all instantial neighbourhood logics and their corresponding multi-conclusion consequence relations. Moreover, we define co-stable canonical formulas to axiomatize all splittings in the lattice ExtINL of instantial neighbourhood logics.

Item Type: Report
Report Nr: MoL-2016-21
Series Name: Master of Logic Thesis (MoL) Series
Year: 2016
Uncontrolled Keywords: Classical modal logics, Instantial Neighbourhood Logic, neighbourhood frames, canonical rules and formulas, splittings
Subjects: Logic
Depositing User: Dr Marco Vervoort
Date Deposited: 12 Jan 2017 15:24
Last Modified: 12 Jan 2017 15:24
URI: https://eprints.illc.uva.nl/id/eprint/1517

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