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Formalizing the plot of Giani Schichi

	In the plot of a story, only a very partial world is created.
Many questions that might be asked about a real situation have
no answers, because nothing the author has written implies an answer or even that
he even thought about the question.  Nevertheless, the reader or
listener can follow the plot.  This suggests that it might be
worthwhile to try to formalize such plots in order to see how to
deal with partial information.  Melodramas provide the clearest
examples, since the motivations of the characters are usually
unproblematical, and the reader understands the plot completely
by the end.

	The opera Gianni Schichi by xxx provides one interesting
example:

	The relatives crowd around the death bed of xxx who has just
died and find his will.  They are disappointed to discover that he
has left his property to a monastery, and they call in the clever
Giani Schichi and ask him if anything can be done.  Schichi asks if
anyone else knows that xxx has died, and they say know.  Schichi then
proposes that he get in the bed, the relatives call the lawyers, and
Schichi will pretend to be xxx and dictate a new will leaving the
property to the relatives.  As proposed Schichi gets in the bed and
the lawyers are called, but Schichi dictates a will leaving the
property to himself.  The relatives don't dare expose him, because
this will expose themselves.

	Here are some considerations concerning the formalization:

	1. It should be divided into two parts - formalization
of the particular facts and formalization of the relevant common
sense knowledge.  Both should be plausible representations of
the knowledge expressed.  In particular the common sense knowledge
should not be ad hoc for the problem.  Ideally, the conditions
for the successful performance of actions should be extracted from
people who don't know that this particular opera is being formalized.
Ideally, the people who formalize the particular facts should not
know in advance the way the common sene knowledge is formalized,
although both groups must be given the same predicate names.

	2. Non-monotonic reasoning, e.g. circumscription will have
to be employed in deducing that the actors can expect to achieve
their goals.  Clearly they cannot deduce that nothing can go wrong,
and a key piece of non-monotonic reasoning is that whereby the
relatives expect to get the property, %2not taking into account%1
the possibility that Schichi may double cross them.
(They don't think of it - not merely assign it a low probability).

	3. The following bits of reasoning occur.

		a. The relatives conclude that if the will is obeyed,
they will be disappointed.

		b. They conclude that the clever Schichi may save
them.  This reasoning has to occur in the face of their not seeing
any way out themselves.

		c. They conclude that Schichi's announced plan can work
work and result in their getting the property.

		d. Schichi reasons that he can will the property to
himself and that the relatives cannot denounce him.  I don't know
if the opera explains that he can arrange that they can't murder him
either if he leaves a document denouncing them.

		e. The whole story slides non-monotonically past the
fact that any unknown third party who knows the story can blackmail
Schichi if he can keep his anonymity so that the revenge against
the relatives won't affect him, and that the relatives can use this
fact to get some of the property back at some risk to themselves.

	All this formalization seems very difficult, so we should
settle for some part of it.  Perhaps the most interesting and
illustrative would be the relatives' expectation of getting the
property, since it contains the subsequently refuted jumping to
a conclusion.

	We will try to use a formalism in which ⊗propositions are
built from predicates, functions, variables and names in the
usual ways - attempting to avoid quantifiers and variables at
first, but the values of these propositions aren't truth values,
but entities that can be given different semanticses by different
%2true(proposition,context)%1 predicates.

Common sense

	Those whom the will says get the property get it.

	Those whom the document accepted as the will says get the
property get it.  Remark: The second statement is a modification
of the first excited by the particular situation.  Perhaps it is
better said more generally.  If one document is accepted as another,
it determines the outcome as though it were.

	Those whom the will says get the property are supposed to
get it.

	The law will give the property to whomever the judge thinks
is supposed to get it.