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Re: [ontolog-forum] CL, CG, IKL and the relationship between symbols in

To: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: "John F. Sowa" <sowa@xxxxxxxxxxx>
Date: Tue, 08 Jan 2008 09:47:29 -0500
Message-id: <47838D01.3060402@xxxxxxxxxxx>
Pat, John B., et al.,    (01)

I have been traveling for the past few days and unable to comment
on the many email notes on this thread.  In general, I support the
points that Pat has made, and I'd like to add some further comments.    (02)

On Dec. 30 and 31, Pat, Chris M., and I exchanged a few notes about
contexts, in which I recommended the use of a box or other delimiter
to enclose a some statement (or conjunction of statements) in some
logical notation.  Following is a brief summary:    (03)

  1. The delimiter, which I represent by a box in conceptual graphs,
     is a purely syntactic mechanism, which can be mapped to the
     IKL construct marked by the keyword 'that'.    (04)

  2. The CG box or the IKL expression "(that *any IKL sentence* )"
     mark the statement of a proposition that can describe any of
     the many different kinds of so-called contexts.    (05)

  3. There have been many different proposals for "context logics",
     but no agreement on which, if any, is suitably general to be
     accepted as a standard.    (06)

  4. However, a CG box or an IKL that-expression appear to be
     sufficiently general to formalize most (perhaps all) of the
     many versions of context logics that have been proposed.    (07)

  5. Sometimes a single sentence in English (or other language,
     natural or artificial) may contain two or more clauses
     that assert propositions that are interpreted in different
     ways in various context logics.    (08)

  6. As an example of such a sentence, I mentioned    (09)

        Tom convinced Sam that it's impossible for
        a cow to jump over the moon.    (010)

     To avoid getting into formal details, I put brackets around
     parts of that sentence to mark different "contexts":    (011)

        [Tom convinced Sam that [it's impossible for
           [a cow to jump over the moon] ] ].    (012)

  7. In a logic such as IKL or CGs, it's possible to state axioms
     for verbs such as 'convince' that determine how the nested
     expressions are interpreted.    (013)

  8. Among the many related issues are various ways of referring
     to "contexts", things in them, and statements that describe
     them, as Pat has discussed in detail in the previous notes.    (014)

Instead of writing anything more right now, I'd prefer to quote
the following excerpts from Ch. 5 of my KR book.    (015)

John Sowa
_________________________________________________________________    (016)

 From Chapter 5, "Purposes, Contexts, and Agents", of the book
_Knowledge Representation_ by J. F. Sowa, Sections 5.2 and 5.3.    (017)

5.2 Syntax of Contexts    (018)

The word 'context' has been used with a variety of conflicting meanings 
in linguistics, philosophy, and artificial intelligence.  Some of the 
confusion results from an ambiguity in the English word.  Dictionaries 
list two major senses of the word 'context':    (019)

     * The basic meaning is a section of linguistic text or discourse 
that surrounds some word or phrase of interest.    (020)

     * The derived meaning is a nonlinguistic situation, environment, 
domain, setting, background, or milieu that includes some entity, 
subject, or topic of interest.    (021)

The word 'context' may refer to the text, to the information contained 
in the text, to the thing that the information is about, or to the 
possible uses of the text, the information, or the thing itself.  The 
ambiguity about contexts results from which of these aspects happens to 
be the central focus.  These informal senses of the word suggest 
criteria for distinguishing the formal functions:    (022)

     * Syntax.  The syntactic function of context is to group, delimit, 
quote, or package a section of text.    (023)

     * Semantics.  The quoted text may describe or refer to some real or 
hypothetical situation.  That nonlinguistic referent is the derived 
meaning of the word context.    (024)

     * Pragmatics. The word 'interest', which occurs in both senses of 
the English definition, suggests some reason or purpose for 
distinguishing the section of linguistic text or nonlinguistic 
situation.  That purpose is the pragmatics or the reason why the text is 
being quoted.    (025)

In LISP, a context is represented by the quote operator, which blocks an 
expression from being executed as a program.  In logic, a quote blocks 
the standard rules of inference and allows the definition of new rules 
for interpreting the text.  In general, a context delimits text that is 
interpreted by some special rules for some particular purpose.  Purpose 
is the central issue that must be distinguished in any formal theory of 
context....    (026)

5.3 Semantics of Contexts    (027)

As William James (1897) observed, an arbitrary region of space-time has 
no intrinsic meaning.  The best way to deal with the bewildering 
confusion of events in some region of space and time is to "break it.... 
We make ten thousand separate serial orders of it, and on any one of 
these we react as though the others did not exist."  A context is a 
package of information about one of those separated chunks of the world. 
Semantics determines how those packages relate to those chunks.    (028)

Situations and Propositions.  Logicians such as Saul Kripke (1963a,b) 
and Richard Montague (1974) developed theories of semantics based on 
models of possible worlds.  Each model represents an unbounded region of 
space-time with all the heterogeneous complexity of William James's 
example.  To avoid such large, open-ended models, Jon Barwise and John 
Perry (1983) developed situation semantics as a theory that relates the 
meaning of sentences to smaller, more manageable chunks called 
'situations'. Each situation is a configuration of some aspect of the 
world in a bounded region of space and time.  It may include people and 
things with their actions and speech; it may be real or imaginary; and 
its time may be past, present, or future.    (029)

Situation semantics is a theory about the flow of information: from 
situations in the world, to speakers who perceive and talk about those 
situations, to listeners who interpret the speech by thinking about and 
acting upon the situations.    (030)

     * Speaker's information flow:  Situation ? Perception ? Statement.    (031)

     * Listener's information flow:  Statement ? Interpretation ? Action
       ? Modified situation.    (032)

This flow relates the abstract symbols of language to the physical 
situations people live in and talk about. Without the physical 
situations at both ends, the symbols would be ungrounded. Symbols 
acquire meaning by the process of symbol grounding, which as Peirce 
insisted depends on triadic relationships:  the speaker expresses a 
*concept* of an *object* by a *symbol*, which the listener interprets by 
an equivalent concept "or perhaps a more developed one."    (033)

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