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C00002 00002	more[f82,jmc]		More on Circumscription
C00003 00003	Each of the several papers that introduces a mode of non-monotonic reasoning
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more[f82,jmc]		More on Circumscription

Abstract: (McCarthy 1980) introduced circumscription as a method
of non-monotonic reasoning.  The present paper contains a new
version of circumscription based on the minimization of formulas
rather than predicates, the notion of prioritized circumscription,
some progress towards heuristics for the use of circumscription
and a discussion of several questions that have arisen concerning
circumscription and other modes of non-monotonic reasoning.
The present paper is logically self-contained, but the motivational
remarks of the previous paper are not repeated or superseded.
Each of the several papers that introduces a mode of non-monotonic reasoning
seems to have a particular application in mind.  Perhaps we are looking
at different parts of an elephant.  Here is a typology of non-monotonic
reasoning about which I solicit comments.  This is intended as part of
a larger paper.  The orientation is towards circumscription, but I suppose
the considerations apply to other formalisms as well.

Circumscription may have several uses.

1. As a communication convention.  Suppose  A  tells  B  about
a situation involving a bird.  If the bird may not be able to fly, and this
is relevant to solving the problem, then  A  should mention
the relevant information.  Whereas if the bird can fly, there is
no requirement to mention the fact.
The circumscriptions to be made by the recipient of the communication
are those described in this paper.  I have not yet considered how
the sender computes what to say and how this refrains from saying
that the bird can fly - presumably without any explicit decision.

2. As a database or information storage convention.  It may be a
convention of a particular database that certain predicates have
their minimal extension.  This generalizes the closed world
assumption.  When a database makes the closed world assumption
for all predicates it is reasonable to imbed this fact in the
programs that use the database.
However, when there
is a priority structure among the predicates, we need to express
the priorities as sentences of the database, perhaps included
in a preamble to it.

Neither 1 nor 2 requires that most birds can fly.
Should it happen that most birds that are subject to the communication
or about which information is requested from the data base cannot fly, the
convention may lead to inefficiency but not incorrectness.

3. As a rule of conjecture.  This use was emphasized
in (McCarthy 1980).  The circumscriptions may be regarded as expressions of some
probabilistic notions such as "most birds can fly" or they may be
expressions of simple cases.  Thus it is simple to conjecture that
there are no relevant present
material objects other
than those whose presence can be inferred.  It is also
a simple conjecture that a tool asserted to be present is usable
for its normal function.  Such conjecture sometimes conflict, but there
is nothing wrong with having incompatible conjectures on hand.  Besides
the possibility of deciding that one is correct and the other wrong, it
is possible to use one for generating possible exceptions to the other.

4. As a representation of a policy.  The example is Doyle's "The meeting
will be on Wednesday unless another decision is explicitly made".

5. As a very streamlined expression of probabilistic information when
numerical probabilities, especially conditional probabilities, are
unobtainable.  Since circumscription doesn't provide numerical probabilities,
its probabilistic interpetation involves
probabilities that are either infinitesimal, within an
infinitesimal of one, or intermediate - without any discrimination
among the intermediate values.  The circumscriptions give conditional
probabilities.  Thus we may treat the probability that a bird
can't fly as an infinitesimal.  However, if the rare
event occurs that the bird is a penguin, then the conditional probability that
it can fly is infinitesimal, but we may hear of some rare condition
that would allow it to fly after all.

	Why don't we use finite
probabilities combined by the usual laws?  That would be fine
if we had the numbers, but circumscription is usable when we can't
get the numbers or find their use inconvenient.  Note that the
general probability that a bird can fly may be irrelevant, because
we are interested in particular situations which weigh in favor or
against a particular bird flying.

	Notice that circumscription does not provide for
weighing evidence; it is appropriate
when the information permits snap decisions.  However, many
cases nominally treated in terms of weighing information are in fact
cases in which the weights are such that circumscription and other
defaults work better.

6. We might also speculate that certain laws of common sense physics
or common sense psychology are inherently non-monotonic or, more specifically,
involve circumscription.  The speculation is that this common sense
information has some inherently preferred form.

	Six different uses for non-monotonic reasoning seem
too many, so perhaps we can condense them.