Belief Functions and Default Reasoning
S. Benferaht, A. Saffiotti, and P. Smets
We present a new approach to deal with default information based on the
theory of belief functions. Our semantic structures, inspired by Adams'
epsilon semantics, are epsilon-belief assignments, where mass values are
either close to 0 or close to 1. In the first part of this paper, we show
that these structures can be used to give a uniform semantics to several
popular non-monotonic systems, including Kraus, Lehmann and Magidor's
system P, Pearl's system Z, Brewka's preferred sub-theories, Geffner's
conditional entailment, Pinkas' penalty logic, possibilistic logic, and
the lexicographic approach. In the second part, we use epsilon-belief
assignments to build a new system, called LCD, and we show that this
system correctly addresses the well-known problems of specificity,
irrelevance, blocking of inheritance, ambiguity, and redundancy.