Generating Explicit Orderings for Non-monotonic Logics

For non-monotonic reasoning, explicit orderings
over formulae offer an important solution to prob-
lems such as ‘multiple extensions’. However, a
criticism of such a solution is that it is not clear,
in general, from where the orderings should be
obtained. Here we show how orderings can be de-
rived from statistical information about the do-
main which the formulae cover. For this we
provide an overview of prioritized logics-a gen-
eral class of logics that incorporate explicit or-
derings over formulae. This class of logics has
been shown elsewhere to capture a wide variety of
proof-theoretic approaches to non-monotonic rea-
soning, and in particular, to highlight the role of
preferences-both implicit and explicit-in such
proof theory. We take one particular prioritized
logic, called SF logic, and describe an experimen-
tal approach for comparing this logic with an im-
portant example of a logic that does not use ex-
plicit orderings of preference-namely Horn clause
logic with negation-as-failure. Finally, we present
the results of this comparison, showing how SF
logic is more skeptical and more accurate than negation-as-failure