A Theory of Hierarchical Consequence and Conditionals

  • Authors:
  • Dov M. Gabbay;Karl Schlechta

  • Affiliations:
  • Department of Computer Science, King's College London, London, UK WC2R 2LS and Department of Computer Science, Bar-Ilan University, Ramat-Gan, Israel 52900;Laboratoire d'Informatique Fondamentale de Marseille, UMR 6166, CNRS and Université de Provence, Marseille Cedex 13, France 13453

  • Venue:
  • Journal of Logic, Language and Information
  • Year:
  • 2010

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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.