On polarity-based semantics for non-distributive modal logics

Abstract

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.