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C00002 00002	contex[s85,jmc]		Notes on contexts
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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 an opration
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.

We have formulas

true(p,c)
value(exp,c)

Let  c0 = context(my 1958 paper)

true(at(I,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.  This domain need not be strings and need not even be
countable.

	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.

	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.

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.