On polarity-based semantics for non-distributive modal logics
| dc.contributor.advisor | Conradie, Willem | |
| dc.contributor.author | Clingman, R. | |
| dc.date.accessioned | 2024-05-16T10:51:24Z | |
| dc.date.available | 2024-05-16T10:51:24Z | |
| dc.date.issued | 2023 | |
| dc.description | A dissertation submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg, in fulfilment of the requirements for the degree of Master of Science. | |
| dc.description.abstract | This masters study builds upon recent research in polarity-based semantics for non-distributive modal logics (NDMLs). Current formulations of polarity-based semantics for NDML impose compatibility requirements on additional relations of polarity-based frames, hindering applicability of the semantics, as arbitrary frames need not be compatible. In this study we develop a polarity-based semantics for NDML with modalites that are, in general, neither normal nor distributive and without the imposition of compatibility requirements. We provide a sound and complete axiomatization of this logic. The second half of the thesis focuses on a special class of enriched polarities, those who are in a sense liftings of Kripke frames. The compatibility of these liftings combined with the intuitive nature of the underlying Kripke frames makes for a useful case study in which to explore p-morphisms between enriched polarities, and enriched polarity-based models, from a relational perspective. | |
| dc.description.librarian | PM2024 | |
| dc.description.sponsorship | National Research Foundation (NRF) | |
| dc.faculty | Faculty of Science | |
| dc.identifier.uri | https://hdl.handle.net/10539/38483 | |
| dc.language.iso | en | |
| dc.publisher | University of the Witwatersrand, Johannesburg | |
| dc.rights | © 2023 University of the Witwatersrand, Johannesburg | |
| dc.rights.holder | University of the Witwatersrand, Johannesburg | |
| dc.school | School of Mathematics | |
| dc.subject | Modal logic | |
| dc.subject | Logic | |
| dc.subject | Non-distributive modal logic | |
| dc.subject | Non-classic logic | |
| dc.subject.other | SDG-17: Partnerships for the goals | |
| dc.title | On polarity-based semantics for non-distributive modal logics | |
| dc.type | Dissertation |