A Dissertation submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg, in ful lment of the requirements for the degree of Master of Science in Mathematics. 26 August 2016. / In this thesis we analyse the issue of decidability for two modal logics which contain least binders.
Towards this goal, we begin the work with a brief survey of modal logic, PDL, the modal -calculus
and algebraic filtrations as exposited by Conradie et al. The first such modal logic we analyse is
the fragment of the modal -calculus corresponding to PDL; the second logic is the equational
theory of the class of -algebras (motivated by the least root calculus of Pratt). We offer a new,
algebraic, proof for the decidability of PDL by showing that PDL has the finite model property
with respect to the class of dynamic algebras. We then show that the equational theory of the class
of -algebras has the finite model property with respect to the class of -algebras; this is based on
the proof of Pratt but differs in an important detail. The finite model property results for these
two modal logics are achieved by an algebraic filtration method based on that of Conradie et al. / LG2017
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:wits/oai:wiredspace.wits.ac.za:10539/21724 |
| Date | January 2016 |
| Creators | Cromberge, Michael Benjamin |
| Source Sets | South African National ETD Portal |
| Language | English |
| Detected Language | English |
| Type | Thesis |
| Format | Online resource (iv, 81 leaves), application/pdf |
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