  In the middle of the 1980s, David Poole introduced a semantical,
model-theoretic notion of specificity to the artificial-intelligence community.
Since then it has found further applications in non-monotonic reasoning, in
particular in defeasible reasoning. Poole tried to approximate the intuitive
human concept of specificity, which seems to be essential for reasoning in
everyday life with its partial and inconsistent information. His notion,
however, turns out to be intricate and problematic, which --- as we show ---
can be overcome to some extent by a closer approximation of the intuitive human
concept of specificity. Besides the intuitive advantages of our novel
specificity ordering over Poole's specificity relation in the classical
examples of the literature, we also report some hard mathematical facts:
Contrary to what was claimed before, we show that Poole's relation is not
transitive. The present means to decide our novel specificity relation,
however, show only a slight improvement over the known ones for Poole's
relation, and further work is needed in this aspect.
