Article

Journal of Logic, Language and Information

, 19:3

First online:

A Theory of Hierarchical Consequence and Conditionals

  • Dov M. GabbayAffiliated withDepartment of Computer Science, King’s College LondonDepartment of Computer Science, Bar-Ilan University Email author 
  • , Karl SchlechtaAffiliated withLaboratoire d’Informatique Fondamentale de Marseille, UMR 6166, CNRS and Université de Provence

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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.

Keywords

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