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C00002 00002	contex[s85,jmc]		Notes on contexts
C00011 00003	How about formalizing some part of a story from Joyce's Dubliners, e.g.
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contex[s85,jmc]		Notes on contexts

	The idea most worth exploring for formalization of common
sense is a generalized notion of context.  There should be operations
of moving detail between a sentence and the context.  Also domains
for variables can be included in the context so that the truth of
a quantified "internal language assertion" can be translated to a
first order formula.

	In various places in this note, we use English expressions,
and many of the concepts used take the form of translations of English
expressions.  However, in order to avoid confusion between this research
and the much more extensive research in formalization of natural language,
we must explain that our objective isn't formalization of English.
Rather it is to capture in a formal language certain classes of concepts
used in natural language that are useful for an artificial intelligence
whether or not it ever communicates in natural language with humans.

In the following formulas  p  is a proposition,  exp  is an
expression representing an individual concept and  c  is a context.

true(p,c) asserts that  p  is true in context  c.

value(exp,c)  is the value of the expression  exp  in context  c.

Let  c0 = context(my 1958 paper)

true(at(I,the(Airport)),c0)
 ≡ true(timed(1958 Aug 15,at(JMC,Westchester Airport)),c0)

but besides  c0  there are some less specified contexts in which it is
true.  A treatment of quantified assertions may be based on

true(All(X,E),c)
  ≡ ∀x.x ε domain(X,c) ⊃ true(subst(name(x),X,E),c).

Here  name(x)  takes the object  x  into some abstract domain of name
expressions.  The domain of expressions  E  need not be thought of as
consisting of strings of symbols.  For example, they may be extensional
forms in which bound variables disappear, e.g. All(X,E) doesn't contain
X  and in which expressions  E1  and  E2  are the same if they have
the same value for all assignments of values to their bound variables.
However, they are built up from variables, constants and functions,
and the result of substituting an expression for a variable in another
must be meaningful.
The domain of names need not be strings and need not even be
countable.  Attaching domains to contexts is apparently an innovation,
but it seems essential.

****
	We would like to extract finite "models", e.g. of the Missionaries
and Cannibals (M&C) problem, out of of contexts.

	We may have predicates and functions apart from  true  and   value
on contexts.  However, every sentence involving these other predicates
and functions should be equivalent to a sentence of form  true(p,c')  where
c'  is a "wider" context.

	The extraction of finite sentential "models" from collections
of sentences in contexts seeems to be a non-monotonic process, but perhaps
this isn't quite true.  Namely, the context may itself warrant the
circumscription sentences that ordinarily constitute a non-monotonic step.
Another way of putting this: An inference that is non-monotonic in one
context may be monotonic in a wider context, because the wider context
may refer explicitly to minimizing abnormality in the narrow context taking
the set of sentences obtained in a certain way into account.  Admittedly
this is vague; the reader is challenged to try to make some sense out of it.

	We can create "inner contexts" that are associated with statements,
beliefs, hopes and stories.

	We can treat contexts as objective or subjective as suits best what
we want to say.

	We also need to carve out situations and events as functions on
contexts.  There can be unknown aspects of a context, e.g. unknown
properties of natural kinds.

airport is a concept
the(airport) is a related concept
Westchester County Airport is another concept
value(the(airport),c) = value(Westchester County Airport,c)

	We introduce the predicate  means(exp1,exp2,c)  to assert
that  exp1  means  exp2  in context  c.  For example, we may have

	means(the(airport),Westchester County Airport,c0).

We could have

	value(the(airport),c) = Westchester County Airport,

but then we are committed to Westchester County Airport as a
concept independent of context.  Perhaps we are committed only
locally, i.e. whatever concepts are mentioned in a discourse
are all relative to an "outer context" which can be wrapped
around the discourse any time we want.

Any assertion about the  value(exp,c)  is made in a context
and therefore is relative to this "outer" context.

There are some standard contexts.  An important one is that of
the beginning of a Western culture story.  I say "Western culture",
because I don't want to imply English language, because the context
is one in which the language is irrelevant.  What is important is
how the context requires propositional and other expressions to be
interpreted.  A story can begin, ``In 1836 Davy Crockett was at the
Alamo'' or ``Jesus and Moses were playing golf''.  The first sentence
causes one to expect history and the second causes an expectation of
fantasy, more specifically a joke of a certain genre.
How about formalizing some part of a story from Joyce's Dubliners, e.g.
the one in which the boarding house keeper tolerates an affair of a
boarder with her daughter and then forces him to propose to her.  Joyce
leaves out the scene between the mother and the boarder.  We would
need to formalize yielding to temptation, being of two minds, and not
letting the right hand know what the left hand is doing.

The characters in the story require different degrees of ascription
of mental qualities in order to understand the story.  Mrs Mooney,
her daughter Polly and the boarder Mr Doran require ascription of
hopes, fears, beliefs, etc.  Others like Mr Mooney have only behavior,
indeed only past behavior, i.e. their behavior enters only into
setting the stage for the present situation.  Still others have
propensities to behave that are relevant.

See 1985 June 29 notebook for some notes on the characters.