Generalizing Prioritization (April 28 1991)
by Benjamin N. Grosof
Abstract:
We identify several bases for prioritization information. This
motivates us to generalize the idea of prioritization that was
introduced, in the context of circumscription, by John McCarthy (1986)
and formalized by Vladimir Lifschitz (1985). We show that the
structure of the prioritization partial order (i.e., the partial order
over the set of minimized predicates) was previously restricted in
such a way ("layered" or "stratified") as to be unsuitable for
many applications of default reasoning, including inheritance. We
overcome this by showing how to generalize the prioritization partial
order to be any well-founded (e.g., finite) strict partial order.
We show how to prioritize arbitrary model-preference criteria, and
their syntactic correspondents. One application of this is to
generalize prioritized circumscription. We also develop the concept
of composing prioritization and show how to prioritize preference
criteria expressing internally-prioritized groups of minimized
predicates (or defaults). We show that this enables one to express
hierarchical modularity in the specification of default reasoning.
Our definition of prioritization subsumes, as special cases, several
previous ideas about precedence in the non-monotonic reasoning
literature. It is applicable to any kind of preference criteria, even
those not about models, as long as they obey the properties of
reflexivity and transitivity.
Last update: 1-8-98
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