A Study of Subminimal Logics of Negation and their Modal Companions
Nick Bezhanishvili, Almudena Colacito, Dick de Jongh

Abstract:
We study propositional logical systems arising from the lan- guage of Johansson’s minimal logic and obtained by weakening the re- quirements for the negation operator. Using duality and completeness we prove that there are uncountably many such logical systems. We also give model-theoretic and algebraic definitions of filtration for minimal logic and show that they are dual to each other. These constructions en- sure that the propositional minimal logic has the finite model property. Finally, we define and investigate bi-modal companions with non-normal modal operators for some relevant subminimal systems, and give infinite axiomatizations for these bi-modal companions.