Electronic Theses and Dissertations (Masters)

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Browsing Electronic Theses and Dissertations (Masters) by Keyword "Modal logic"

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    On polarity-based semantics for non-distributive modal logics
    (University of the Witwatersrand, Johannesburg, 2023) Clingman, R.; Conradie, Willem
    This masters study builds upon recent research in polarity-based semantics for non-distributive modal logics (NDMLs). Current formulations of polarity-based semantics for NDML impose compatibility requirements on additional relations of polarity-based frames, hindering applicability of the semantics, as arbitrary frames need not be compatible. In this study we develop a polarity-based semantics for NDML with modalites that are, in general, neither normal nor distributive and without the imposition of compatibility requirements. We provide a sound and complete axiomatization of this logic. The second half of the thesis focuses on a special class of enriched polarities, those who are in a sense liftings of Kripke frames. The compatibility of these liftings combined with the intuitive nature of the underlying Kripke frames makes for a useful case study in which to explore p-morphisms between enriched polarities, and enriched polarity-based models, from a relational perspective.
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    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.