Linking Makinson and Kraus-Lehmann-Magidor preferential entailments
  About ten years ago, various notions of preferential entailment have been
introduced. The main reference is a paper by Kraus, Lehmann and Magidor (KLM),
one of the main competitor being a more general version defined by Makinson
(MAK). These two versions have already been compared, but it is time to revisit
these comparisons. Here are our three main results: (1) These two notions are
equivalent, provided that we restrict our attention, as done in KLM, to the
cases where the entailment respects logical equivalence (on the left and on the
right). (2) A serious simplification of the description of the fundamental
cases in which MAK is equivalent to KLM, including a natural passage in both
ways. (3) The two previous results are given for preferential entailments more
general than considered in some of the original texts, but they apply also to
the original definitions and, for this particular case also, the models can be
simplified.
