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Re: [ontolog-forum] Context [was: Truth]

To: ontolog-forum@xxxxxxxxxxxxxxxx
From: John F Sowa <sowa@xxxxxxxxxxx>
Date: Thu, 26 Jul 2012 07:43:32 -0400
Message-id: <50112D64.1080408@xxxxxxxxxxx>
Pat,    (01)

> My point was that the various *kinds* of context have nothing in common,
> so that any suggested *general* logic of contexts will be vacuous.    (02)

I agree with McCarthy that there are an open-ended number of different
kinds of logics that can use different criteria and axioms for what
is in a context and what can be said in it and about it.    (03)

But this is similar to the discussions we had about models.  As you
know, I tend to drag in Peirce and his method of analysis by triads.
His general principle is that whenever you find two kinds of things
that are related in some way, look for the missing third.    (04)

For example, many people use Peirce's terms 'type' and 'token', but
they don't realize that they're using only two parts of his triad:    (05)

  1. A *mark* X is anything observable that has not been interpreted.    (06)

  2. A *token* Y is some mark X that has been interpreted as an instance
     of some type Z.    (07)

  3. A *type* Z is a pattern, rule, or specification for interpreting
     a mark X as a token Y of type Z.    (08)

In general, the same mark may be interpreted in many different ways
from different points of view for different purposes.  The type is
a specification based on that purpose or point of view.    (09)

For models, I suggested the following definition.  I was inspired
by Petri, who suggested a commonality among the various meanings of
the word 'model'.  I stated the commonality in a Peircean triad:    (010)

  1. An *object* X is any physical thing, event, situation...    (011)

  2. A *model* Y of X is a physical or mathematical construction that
     resembles X according to some specification Z.    (012)

  3. A *specification* Z is a statement of the way X resembles Y.
     Z may be single word, such as "shape", or it may be a detailed
     list of statements in some language, linear or graphic.    (013)

An engineering model has all three parts.  A Tarski-style model has
parts #2 and #3, but it might be used to describe something #1.    (014)

In fact, you could even have a Tarski-style model in which Y
was contained in X.  For example, a model (D,R) could be
a domain D of elements that are identified with parts of the
object X, and R could be a set of relations defined over D.
The model would still have three components X, Y, and Z,
but Z would specify how parts of X were selected for Y.    (015)

Given this preamble, I would use the notion of model defined
above to state a general definition of a context for a text:    (016)

  1. A *text* X is a statement in some language, natural or artificial.    (017)

  2. A *context* Y for X is a model (X', Y', Z') plus a mapping of
     of every referring expression in X to something in Y'.    (018)

  3. An *interpretation* of X in terms of Y is the truth value of
     X as determined by the model Y and the mapping in point #2.    (019)

This is an informal, but very general statement that relates
contexts to models.  I believe that it can be formalized in a way
that is compatible with the wide range of applications that various
people have claimed -- including John McCarthy.    (020)

John    (021)

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