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We provide a generalisation of Kripke semantics for an extension of intuitionistic Łukasiewicz logic ( \(\textbf{LLi}\) ) with weak excluded middle ( \(\textbf{LLi}_{\textbf{WEM}}\) ). This analogises the situation with intuitionistic logic ( \(\textbf{IL}\) ) extended by weak excluded middle ( \(\textbf{WEM}\) ). This paper extends the insights of [8] regarding \(\textbf{LLi}\) to \(\textbf{LLi}_{\textbf{WEM}}\) .

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A Kripke Semantics for Intuitionistic Łukasiewicz Logic with Weak Excluded Middle

  • 会议论文

  • 发表日期：

    2026年

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  • Andrew Lewis-Smith,
  • Zhiguang Zhao

摘要

We provide a generalisation of Kripke semantics for an extension of intuitionistic Łukasiewicz logic ( \(\textbf{LLi}\) ) with weak excluded middle ( \(\textbf{LLi}_{\textbf{WEM}}\) ). This analogises the situation with intuitionistic logic ( \(\textbf{IL}\) ) extended by weak excluded middle ( \(\textbf{WEM}\) ). This paper extends the insights of [8] regarding \(\textbf{LLi}\) to \(\textbf{LLi}_{\textbf{WEM}}\) .