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A Theory of Hierarchical Consequence and Conditionals

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Abstract

We introduce \({\mathcal{A}}\) -ranked preferential structures and combine them with an accessibility relation. \({\mathcal{A}}\) -ranked preferential structures are intermediate between simple preferential structures and ranked structures. The additional accessibility relation allows us to consider only parts of the overall \({\mathcal{A}}\) -ranked structure. This framework allows us to formalize contrary to duty obligations, and other pictures where we have a hierarchy of situations, and maybe not all are accessible to all possible worlds. Representation results are proved.

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Authors and Affiliations

  1. Department of Computer Science, King’s College London, Strand, London, WC2R 2LS, UK

    Dov M. Gabbay

  2. Department of Computer Science, Bar-Ilan University, 52900, Ramat-Gan, Israel

    Dov M. Gabbay

  3. Laboratoire d’Informatique Fondamentale de Marseille, UMR 6166, CNRS and Université de Provence, CMI, 39, rue Joliot-Curie, 13453, Marseille Cedex 13, France

    Karl Schlechta

Authors
  1. Dov M. Gabbay
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  2. Karl Schlechta
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Correspondence to Dov M. Gabbay.

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Gabbay, D.M., Schlechta, K. A Theory of Hierarchical Consequence and Conditionals. J of Log Lang and Inf 19, 3–32 (2010). https://doi.org/10.1007/s10849-009-9096-7

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  • DOI: https://doi.org/10.1007/s10849-009-9096-7

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