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A many-dimensional approach to simulations in modal logic
Thesis (MSc)--Stellenbosch University, 2012.
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| Format: | Thesis |
| Language: | en_ZA |
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Stellenbosch : Stellenbosch University
2012
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| _version_ | 1867614026871078912 |
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| access_status_str | Open Access |
| author | Cloete, Walter (Walter Theophilus Woldemar) |
| author2 | Rewitzky, I. M. |
| author_browse | Cloete, Walter (Walter Theophilus Woldemar) Rewitzky, I. M. |
| author_facet | Rewitzky, I. M. Cloete, Walter (Walter Theophilus Woldemar) |
| author_sort | Cloete, Walter (Walter Theophilus Woldemar) |
| collection | Thesis |
| dc_rights_str_mv | Stellenbosch University |
| description | Thesis (MSc)--Stellenbosch University, 2012. |
| format | Thesis |
| id | oai:scholar.sun.ac.za:10019.1/20152 |
| institution | Stellenbosch University (South Africa) |
| language | en_ZA |
| last_indexed | 2026-06-10T12:45:30.338Z |
| license_str | Other — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from SUNScholar — Stellenbosch University Repository |
| publishDate | 2012 |
| publishDateRange | 2012 |
| publishDateSort | 2012 |
| publisher | Stellenbosch : Stellenbosch University |
| publisherStr | Stellenbosch : Stellenbosch University |
| record_format | dspace |
| source_str | SUNScholar — Stellenbosch University Repository |
| spelling | oai:scholar.sun.ac.za:10019.1/20152 A many-dimensional approach to simulations in modal logic Cloete, Walter (Walter Theophilus Woldemar) Rewitzky, I. M. Stellenbosch University. Faculty of Science. Dept. of Mathematical Sciences. Modal logic Kripke frame Bisimulation Dissertations -- Mathematics Theses -- Mathematics Frame products Thesis (MSc)--Stellenbosch University, 2012. ENGLISH ABSTRACT: Truth preservation is an important topic in model theory. However a brief examination of the models for a logic often show that isomorphism is needlessly restrictive as a truth preserving construction. In the case of modal logics with Kripke semantics the notions of simulation and bisimulation prove far more practical and interesting than isomorphism. We present and study these various notions, followed by a discussion of Shehtman’s frame product as semantics for certain many-dimensional modal logics. We show how simulations and bisimulations can be interpreted inside models over frame products. This is followed by a discussion on a category-theoretic setting for frame products, where the arrows may run between frames with different types. AFRIKAANSE OPSOMMING: Die behou van waarheid is ’n prominente onderwerp in modelteorie. ’n Vlugtige ondersoek van die modelle vir ’n besondere logika wys egter dat isomorfisme onnodig beperkend as waarheid-behoudende konstruksie is. In die geval van modale logika met Kripke se semantiek is simulasie en bisimulasie heelwat meer prakties en interessant as isomorfisme. Na die bekendstel en studie van hierdie onderskeie begrippe bespreek ons Shehtman se raamproduk as semantiek vir sekere meer-dimensionele modale logikas. Ons wys ons hoe simulasies en bisimulasies binne modelle oor sulke raamprodukte geïnterpreteer kan word. Daarna bespreek ons ’n kategorie-teoretiese konteks vir raamprodukte, waar die pyle tussen rame met verskillende tipes mag loop. 2012-03-05T07:14:02Z 2012-03-30T10:47:29Z 2012-03-05T07:14:02Z 2012-03-30T10:47:29Z 2012-03 Thesis http://hdl.handle.net/10019.1/20152 en_ZA Stellenbosch University 83 p. : ill. application/pdf Stellenbosch : Stellenbosch University |
| spellingShingle | Modal logic Kripke frame Bisimulation Dissertations -- Mathematics Theses -- Mathematics Frame products Cloete, Walter (Walter Theophilus Woldemar) A many-dimensional approach to simulations in modal logic |
| title | A many-dimensional approach to simulations in modal logic |
| title_full | A many-dimensional approach to simulations in modal logic |
| title_fullStr | A many-dimensional approach to simulations in modal logic |
| title_full_unstemmed | A many-dimensional approach to simulations in modal logic |
| title_short | A many-dimensional approach to simulations in modal logic |
| title_sort | many dimensional approach to simulations in modal logic |
| topic | Modal logic Kripke frame Bisimulation Dissertations -- Mathematics Theses -- Mathematics Frame products |
| url | http://hdl.handle.net/10019.1/20152 |
| work_keys_str_mv | AT cloetewalterwaltertheophiluswoldemar amanydimensionalapproachtosimulationsinmodallogic AT cloetewalterwaltertheophiluswoldemar manydimensionalapproachtosimulationsinmodallogic |