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In this work, we propose using possibility theory to represent a belief base and to reason over it, particularly in the presence of inconsistencies. We revisit semantics from the existing literature and introduce two additional properties that help to clarify how these semantics are interconnected. The framework is then restricted to hypotheses expressed as linear numerical inequalities, in order to benefit from the polynomial-time complexity of Linear Programming while maintaining possibilistic reasoning. Finally, we define certified inference syntaxes based on Farkas’ Lemma, allowing a certificate to be provided for each inference.

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Possibilistic Logic and Inference for Linear Systems

  • 会议论文

  • 发表日期：

    2026年

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  • Armand Gaudillier,
  • Khaled Belahcène,
  • Wassila Ouerdane,
  • Sébastien Destercke

摘要

In this work, we propose using possibility theory to represent a belief base and to reason over it, particularly in the presence of inconsistencies. We revisit semantics from the existing literature and introduce two additional properties that help to clarify how these semantics are interconnected. The framework is then restricted to hypotheses expressed as linear numerical inequalities, in order to benefit from the polynomial-time complexity of Linear Programming while maintaining possibilistic reasoning. Finally, we define certified inference syntaxes based on Farkas’ Lemma, allowing a certificate to be provided for each inference.