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Re: [ontolog-forum] Scheduling a Discussion [was: CL, CG, IKL and the re

To: "Peter Yim" <peter.yim@xxxxxxxx>
Cc: "[ontolog-forum] " <ontolog-forum@xxxxxxxxxxxxxxxx>
From: Pat Hayes <phayes@xxxxxxx>
Date: Wed, 2 Jan 2008 18:07:38 -0800
Message-id: <p06230915c3a1e5b1ef2c@[]>
>  > [DN]  Would make an interesting ontolog session sometimes in 2008.
>>  Maybe Peter can schedule a call.
>[ppy] Sure, I'd be most happy to. I'd need a more refined statement of
>WHAT (exactly) it is, that folks would like to discuss, and WHO are
>the people they would like to hear from (or hear discussing the issue
>at hand).
>Are we going for CL, CG, IKL and the relationship between symbols in
>the logical "universe of discourse" and individuals in the "real
>world"? Representing Context in general? How CL/IKL deals with
>context? ...
>I solicit input from those interested on:
>(a) A clear statement of the "topic",    (01)

FWIW, this is not a new topic. The general idea of the relevance of 
context in language and KR and logic has been discussed now for 
several decades, including at least one entire series of successful 
interdisciplinary research meetings entirely devoted to it. At one of 
the very first 'ontology summit' meetings (at Heidelburg in, if my 
memory serves me right, 1997), a whole session was devoted to an 
attempt to define and clarify the notion. At least four distinct 
logics for context have been fully developed and at least two of them 
are now deployed in industrial-scale working software systems. So we 
are not, or at least SHOULD not be, working in an entirely new area 
here.    (02)

Unless all the participants are at least marginally aware of all this 
preceding effort and the general shape of the debates that have gone 
on, we will only be repeating history.    (03)

FWIW, here is the definition of "context" that I put forward at 
Heidelberg, and which seemed to meet with some general acceptance.    (04)

Theories of meaning invariably focus their attention on some subset 
of the many factors which can possibly influence the actual meaning 
conveyed by a meaningful utterance or sentence or diagram, or any 
symbolic structure or act. The other factors or aspects which may 
influence meaning, but which are not explicitly examined by the 
theory, are often referred to as "context". Thus, the term "context" 
has no single meaning: it is used simply to refer to anything (or 
sometimes everything) which can influence meaning but which is 
outside the scope of the current theory. It is always defined 
-------    (05)

This means, in turn, that there is no such 'thing' as an objective 
context, and so there is no general theory of contexts, or science of 
contexts, which can be applied to all cases of "context". Indeed, 
since, in the limit, it seems that almost anything can influence 
meaning under some circumstances, it follows that anything at all can 
be considered to be a context. One sees evidence for this conclusion 
by examining the proceedings of any of the 'context workshops', and 
checking carefully what each author means by the word "context". At 
the second such workshop (held at MIT in 2003), every single 
contributing author had a different notion, ranging in scope from a 
single occurrence of a single word in a single sentence (as exhibited 
in so-called 'priming' experiments) to an entire social/cultural 
milieu, such as China in the 13th century.    (06)

Which, to get back to the topic, is why starting a discussion of 
contexts with any attempt to "define the topic" is unlikely to 
succeed, for the very good reason that there really is no such topic. 
(And even if by some miracle it does, that success will only be 
temporary, because you can guarantee that someone else out there will 
disagree.)    (07)

BTW, partly as a reaction to this observation, the formalized 
'context logics' developed by McCarthy, Guha (and John Sowa, though 
he used a different terminology) are deliberately agnostic as to the 
nature of "contexts", and adopt a theoretical stance along the lines 
of: a context is whatever satisfies the axioms of my logic/theory of 
contexts (analogous to a mathematical reply to a question such as 
'what is a commutative algebra?'). However, the apparent 
reasonableness of this 'mathematical' stance is somewhat undermined 
by the fact that none of the extant such logics provide more than one 
or two axioms or principles, and the very few that they have provided 
have obvious, immediate counterexamples in cases that everyone agrees 
should be possible to treat as contexts (such as a time-interval). 
This situation has not changed in about a decade of intensive work on 
these logics, which to my mind at least reduces the 'mathematical 
theory' position to absurdity: apparently, there is no mathematical 
theory of contexts. And calling a diverse collection of things by a 
single name is not good science, nor good engineering, nor good 
methodology. For example, a good deal of the work on "context logic" 
has been a slow rediscovery of ideas that were already well known and 
thoroughly investigated in temporal logic, but because it was seen as 
being about "contexts" instead of mere time-intervals, the earlier 
work (which in many cases was vastly superior, having been done by 
some of the best philosophical logicians of the last century) was 
ignored.    (08)

The more popular recent stance is that there are many kinds of 
context, each with its own axioms and principles: time-intervals, 
time-points, sets of beliefs, linguistic conventions, conversational 
settings, etc.. Well, OK: but all of these (and others) already had 
more or less mature fields investigating them, without using the 
"context" word. So now the question arises, what value is gained by 
using a single term to refer to them all? It suggests a commonality 
which does not appear to be present. Time-intervals and states of 
belief, in particular - the two most commonly suggested "kinds" of 
context - seem to have almost nothing in common at all. If anyone can 
suggest a single axiom which relates propositions or sentences to 
contexts, and is true both when this means the proposition is true at 
or in that time, and also when it means the proposition is entailed 
by a set of beliefs, I would be delighted to be shown it. I have made 
this challenge repeatedly to proponents of 'contexts' for many years, 
and have yet to be given an answer.    (09)

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