Ranking functions and rankings on languages

  • Authors:
  • Franz Huber

  • Affiliations:
  • California Institute of Technology

  • Venue:
  • Artificial Intelligence
  • Year:
  • 2006

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Abstract

The Spohnian paradigm of ranking functions is in many respects like an order-of-magnitude reverse of subjective probability theory. Unlike probabilities, however, ranking functions are only indirectly--via a pointwise ranking function on the underlying set of possibilities W--defined on a field of propositions A over W. This research note shows under which conditions ranking functions on a field of propositions A over W and rankings on a language L are induced by pointwise ranking functions on W and the set of models for L, ModL, respectively.