A Theory of Hierarchical Consequence and Conditionals


DOI: 10.1007/s10849-009-9096-7

Cite this article as:
Gabbay, D.M. & Schlechta, K. J of Log Lang and Inf (2010) 19: 3. doi:10.1007/s10849-009-9096-7


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.


Deontic logic Contrary-to-duties Preferential structures Ranked structures Nonmonotonic logic Representation results 

Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  1. 1.Department of Computer ScienceKing’s College LondonLondonUK
  2. 2.Department of Computer ScienceBar-Ilan UniversityRamat-GanIsrael
  3. 3.Laboratoire d’Informatique Fondamentale de Marseille, UMR 6166CNRS and Université de ProvenceMarseille Cedex 13France

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