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KLM-Style Defeasibility for Restricted First-Order Logic

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Rules and Reasoning (RuleML+RR 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13752))

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Abstract

In this paper, we extend the KLM approach to defeasible reasoning beyond the propositional setting. We do so by making it applicable to a restricted version of first-order logic. We describe defeasibility for this logic using a set of rationality postulates, provide a suitable and intuitive semantics for it, and present a representation result characterising the semantic description of defeasibility in terms of our postulates. An advantage of our semantics is that it is sufficiently general to be applicable to other restricted versions of first-order logic as well. Based on this theoretical core, we then propose a version of defeasible entailment that is inspired by the well-known notion of Rational Closure as it is defined for defeasible propositional logic and defeasible description logics. We show that this form of defeasible entailment is rational in the sense that it adheres to the full set of rationality postulates.

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Acknowledgments

This work was partially supported by the ANR Chaire IA BE4musIA: BElief change FOR better MUlti-Source Information Analysis, and by TAILOR, a project funded by EU Horizon 2020 research and innovation programme under GA No. 952215.

Author information

Authors and Affiliations

  1. ISTI–CNR, Pisa, Italy

    Giovanni Casini, Thomas Meyer & Ivan Varzinczak

  2. University of Cape Town, Cape Town, South Africa

    Giovanni Casini, Thomas Meyer & Guy Paterson-Jones

  3. CAIR, Cape Town, South Africa

    Giovanni Casini, Thomas Meyer, Guy Paterson-Jones & Ivan Varzinczak

  4. LIASD, Université Paris 8, Paris, France

    Ivan Varzinczak

  5. Stellenbosch University, Stellenbosch, South Africa

    Ivan Varzinczak

Authors
  1. Giovanni Casini
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  2. Thomas Meyer
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  3. Guy Paterson-Jones
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  4. Ivan Varzinczak
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Corresponding author

Correspondence to Thomas Meyer .

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Editors and Affiliations

  1. Singapore Management University, Singapore, Singapore

    Guido Governatori

  2. Dresden University of Technology, Dresden, Germany

    Anni-Yasmin Turhan

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Casini, G., Meyer, T., Paterson-Jones, G., Varzinczak, I. (2022). KLM-Style Defeasibility for Restricted First-Order Logic. In: Governatori, G., Turhan, AY. (eds) Rules and Reasoning. RuleML+RR 2022. Lecture Notes in Computer Science, vol 13752. Springer, Cham. https://doi.org/10.1007/978-3-031-21541-4_6

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  • DOI: https://doi.org/10.1007/978-3-031-21541-4_6

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-21540-7

  • Online ISBN: 978-3-031-21541-4

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