Defeasible and Pointwise Circumscription: Preliminary Report
by Benjamin N. Grosof
Abstract:
We suggest why, and show how, to represent defeasible reasoning
about prioritization-type precedence. We define Defeasible
Axiomatized Policy (DAP) circumscription: it is the first formalism to
express defeasible prioritization. DAP circumscription can represent
one or more (generally, a finite reflective tower) of meta-levels of
such reasoning, without resorting to a more powerful logical
language. We argue for the usefulness, and analyze the expressive
significance, of this representational generalization. We show that
it can often be achieved with only a modest increase in the
mathematical complexity of inference: DAP circumscription often
reduces to a series of prioritized predicate circumscriptions, for
which inference procedures are currently available.
DAP circumscription also offers an improved approach to pointwise
prioritization and circumscription, even in the basic, monotonic case
of reasoning about prioritization. We observe that unsatisfiability
and representational awkwardness trouble the previous approach, due to
Lifschitz. DAP circumscription overcomes these difficulties.
Last update: 1-8-98
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