Pointwise Intersection in Neighbourhood Modal Logic

Faculty/Professorship: Political Theory  
Author(s): Van De Putte, Frederik; Klein, Dominik 
Editors: Bezhanishvili, Guram; Studer, Thomas; D'Agostino, Giovanna; Metcalfe, George
Title of the compilation: Advances in Modal Logic
Publisher Information: London : King's College Publications
Year of publication: 2018
Pages: 591-610
Series ; Volume: AiML ; 12
Language(s): English
We study the logic of neighbourhood models with pointwise intersection, as a means to characterize multi-modal logics. Pointwise intersection takes us from a set of neighbourhood sets Ni (one for each member i of a set G used to interpret the modality □) to a new neighbourhood set NG, which in turn allows us to interpret the operator □G Here, X is in the neighbourhood for G if and only if X equals the intersection of some Y {Yi | Yi ∈G}. We show that the notion of pointwise intersection has various applications in epistemic and doxastic logic, deontic logic, coalition logic, and evidence logic. We then establish sound and strongly complete axiomatizations for the weakest logic characterized by pointwise intersection and for a number of variants, using a new and generally applicable technique for canonical model construction.
Keywords: modal logic, neighbourhood semantics, group operators, distributed belief
Peer Reviewed: Ja
International Distribution: Ja
Type: Conferenceobject
URI: https://fis.uni-bamberg.de/handle/uniba/44756
Year of publication: 10. January 2019