A Study of Subminimal Logics of Negation and Their Modal Companions

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11456)


We study propositional logical systems arising from the language of Johansson’s minimal logic and obtained by weakening the requirements for the negation operator. We present their semantics as a variant of neighbourhood semantics. We use duality and completeness results to show that there are uncountably many subminimal logics. We also give model-theoretic and algebraic definitions of filtration for minimal logic and show that they are dual to each other. These constructions ensure 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.



We would like to thank the referees for their careful reading, which has helped us to clarify a number of issues and improve the paper.


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© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Institute for Logic, Language and ComputationUniversity of AmsterdamAmsterdamThe Netherlands
  2. 2.Mathematical InstituteUniversity of BernBernSwitzerland

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