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In this paper, based on duality-theoretic techniques, we introduce a sound and complete neighborhood semantics based on polarities for basic lattice-based monotone modal logic, and show that monotone modal operators in lattice-based monotone modal logic can be represented as the composition of suitable normal modal operators via a multi-type representation of complete lattices with monotone operators.

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Monotone Modal Logic Beyond Distributivity

  • 会议论文

  • 发表日期：

    2025年

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  • Yiwen Ding,
  • Krishna Manoorkar,
  • Alessandra Palmigiano,
  • Ruoding Wang

摘要

In this paper, based on duality-theoretic techniques, we introduce a sound and complete neighborhood semantics based on polarities for basic lattice-based monotone modal logic, and show that monotone modal operators in lattice-based monotone modal logic can be represented as the composition of suitable normal modal operators via a multi-type representation of complete lattices with monotone operators.