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<p>This paper presents a novel proof-theoretic approach to a logic specifically designed to handle exceptions and typicality. Our method extends the classical first-order sequent calculus by incorporating a specialized framework to manage both <i>negative</i> extra-logical information (explicit exceptions) and <i>positive</i> information (background assumptions). We prove that the resulting sequent calculi satisfy the cut-elimination theorem, thereby ensuring strong analytical properties. Furthermore, we show how this framework effectively models traditional reasoning patterns involving conflicting information and typicality. Finally, we establish a natural correspondence between our approach and the Kraus-Lehmann-Magidor postulates, further grounding our work within established theoretical foundations.</p>

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Exception and typicality, logically framed

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年6月12日

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  • Mario Piazza,
  • Matteo Tesi

摘要

This paper presents a novel proof-theoretic approach to a logic specifically designed to handle exceptions and typicality. Our method extends the classical first-order sequent calculus by incorporating a specialized framework to manage both negative extra-logical information (explicit exceptions) and positive information (background assumptions). We prove that the resulting sequent calculi satisfy the cut-elimination theorem, thereby ensuring strong analytical properties. Furthermore, we show how this framework effectively models traditional reasoning patterns involving conflicting information and typicality. Finally, we establish a natural correspondence between our approach and the Kraus-Lehmann-Magidor postulates, further grounding our work within established theoretical foundations.