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Communities in WIReDSpace
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- This community is for all faculties and schools' research outputs and publications by Wits academics and researchers.
- This community hosts traditional outputs such as published and unpublished research articles, conference papers, book chapters and other research outputs authored by Wits academics and researchers. Items in this collection are also mapped to relevant collections within the Faculties/Schools/Departments communities for more specific browsing and searching.
- This Community hosts a collection of electronic theses and dissertations (ETDs) submitted by doctoral and masters' students of Wits University.
- This community is for all faculties and schools' theses and dissertations by masters and doctoral students.
Recent Submissions
Tableaux and Decision Procedures for Many-Valued Modal Logics
(University of the Witwatersrand, Johannesburg, 2024) Axelrod, Guy Ross
The aim of this dissertation is to present results expanding on the work done by Melvin Fitting in [22] and [24]. In [22], Fitting introduces a framework of many-valued modal logics, where modal formulas are interpreted via generalized Kripke models in which both the propositional valuation and the accessibility relation take on values from some Heyting algebra of truth values. For a fixed arbitrary finite Heyting algebra, H, [24] presents a signed semantic tableau system that is sound and complete with respect to all H-frames. We go on to consider the many-valued generalizations of frame properties such as reflexivity and transitivity (as presented in [39]) and give parameterized tableau systems which are sound and complete with respect to classes of H-frames satisfying such properties. Further, a prefixed tableau system is introduced, which allows us to define an intuitive decision procedure deciding the logics of the above- mentioned H-frame classes, as well as logics of H-frames satisfying generalized symmetry properties, which cannot be captured by Fitting’s unprefixed systems. Further, they allow us to derive finite frame properties. Such a decision procedure has been implemented, and is available on GitHub.
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