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To reason about complex systems, logical tools and results provide a fundamental framework for studying regularities in such systems. However, standard approaches, though very successful, assume that transitions can occur only between states that behave according to a single logic. To reason about behaviors of some complex systems, it is worth considering different logics in different states. The issue is how to meaningfully communicate values in different lattices semantics of states’ logics. In this paper, we propose a method, based on the direct product construction, to produce a natural common lattice background in which the relation between the original lattices can be represented.

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Lattices for Many-Logics Modal Logic: Constructions and Representations

  • 会议论文

  • 发表日期：

    2025年

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  • Alfredo Freire,
  • Alexandre Madeira,
  • Manuel A. Martins

摘要

To reason about complex systems, logical tools and results provide a fundamental framework for studying regularities in such systems. However, standard approaches, though very successful, assume that transitions can occur only between states that behave according to a single logic. To reason about behaviors of some complex systems, it is worth considering different logics in different states. The issue is how to meaningfully communicate values in different lattices semantics of states’ logics. In this paper, we propose a method, based on the direct product construction, to produce a natural common lattice background in which the relation between the original lattices can be represented.