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.
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:sun/oai:scholar.sun.ac.za:10019.1/20152 |
| Date | 03 1900 |
| Creators | Cloete, Walter (Walter Theophilus Woldemar) |
| Contributors | Rewitzky, I. M., Stellenbosch University. Faculty of Science. Dept. of Mathematical Sciences. |
| Publisher | Stellenbosch : Stellenbosch University |
| Source Sets | South African National ETD Portal |
| Language | en_ZA |
| Detected Language | English |
| Type | Thesis |
| Format | 83 p. : ill. |
| Rights | Stellenbosch University |
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