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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I would like to thank the anonymous reviewers for many constructive and helpful comments.
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de Groot, J. Positive Monotone Modal Logic. Stud Logica 109, 829–857 (2021). https://doi.org/10.1007/s11225-020-09928-9
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DOI: https://doi.org/10.1007/s11225-020-09928-9