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A many-dimensional approach to simulations in modal logic

dc.contributor.advisorRewitzky, I. M.en_ZA
dc.contributor.authorCloete, Walter (Walter Theophilus Woldemar)en_ZA
dc.contributor.otherStellenbosch University. Faculty of Science. Dept. of Mathematical Sciences.en_ZA
dc.date.accessioned2012-03-05T07:14:02Zen_ZA
dc.date.accessioned2012-03-30T10:47:29Z
dc.date.available2012-03-05T07:14:02Zen_ZA
dc.date.available2012-03-30T10:47:29Z
dc.date.issued2012-03en_ZA
dc.identifier.urihttp://hdl.handle.net/10019.1/20152
dc.descriptionThesis (MSc)--Stellenbosch University, 2012.en_ZA
dc.description.abstractENGLISH 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.en_ZA
dc.description.abstractAFRIKAANSE 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.af_ZA
dc.format.extent83 p. : ill.
dc.language.isoen_ZAen_ZA
dc.publisherStellenbosch : Stellenbosch Universityen_ZA
dc.subjectModal logicen_ZA
dc.subjectKripke frameen_ZA
dc.subjectBisimulationen_ZA
dc.subjectDissertations -- Mathematicsen_ZA
dc.subjectTheses -- Mathematicsen_ZA
dc.subjectFrame productsen_ZA
dc.titleA many-dimensional approach to simulations in modal logicen_ZA
dc.typeThesis
dc.rights.holderStellenbosch University


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