Positive Monotone Modal Logic

Abstract

Positive monotone modal logic is the negation- and implication-free fragment of monotone modal logic, i.e., the fragment with connectives and . We axiomatise positive monotone modal logic, give monotone neighbourhood semantics based on posets, and prove soundness and completeness. The latter follows from the main result of this paper: a (categorical) duality between so-called \(M^+\)-spaces (poset-based monotone neighbourhood frames with extra structure) and the algebraic semantics of positive monotone modal logic. The main technical tool is the use of coalgebra.

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Acknowledgements

I would like to thank the anonymous reviewers for many constructive and helpful comments.

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Correspondence to Jim de Groot.

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de Groot, J. Positive Monotone Modal Logic. Stud Logica (2021). https://doi.org/10.1007/s11225-020-09928-9

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Keywords

  • Positive modal logic
  • Monotone modal logic
  • Coalgebraic logic
  • Duality