On Jul 23, 2012, at 8:16 PM, John F Sowa wrote: (01)
> On 7/23/2012 6:22 PM, Pat Hayes wrote:
>> IKL is CL with the addition of a construct (that <sentence>) which allows
>> the formalism to refer to propositions. GIven that, you can then introduce
>> an *ontology* of things someone might want to call 'contexts' and say that
>> propositions (not sentences) are true or false in them. That was largely
>> the point of inventing IKL in the first place, in fact. But still IKL
>> is not a context *logic*.
>
> I agree with that point.
>
> PH
>> All I said was that CL and IKL are not context logics. You can axiomatize
>> a theory of contexts in them, as you please. I recommend IKL as it has
>> the expressiveness to encode content from just about any context logic
>> (and in many cases, to do a better job, IMO.)
>
> The last time I spoke with John McCarthy was in 2006, during the time of
> the IKRIS project. We had a short, informal meeting at Stanford about
> contexts and the IKRIS project. It included John, his student Selene
> Makarios (who was working on a theory of contexts), and Mike Genesereth. (02)
And me. And it was then that I asked John about his basic logical construct
'ist', written as (03)
ist(c, p) (04)
and read as meaning " p is true in the context c". The question was, is the 'p'
in this formula a sentence or a proposition? It is *written* in the
McCarthy/Guha/Makarios context logics as a sentence; but to my delight, John
said it was a proposition. Which is exactly what it is in the IKL way of
writing this as a logical relation between two things, a context and a
proposition: (05)
(ist c (that p)) (06)
>From which I conclude that the IKL way of writing contextual truths is in fact
>closer to McCarthy's basic ideas than the context logic he developed to
>formally express them. (07)
BTW, JMcC also had a clear answer to the question, what is a context, exactly?
Which was, anything that you can write in the first agument position of an
atomic ist sentence. That is, anything can be considered to be a context. (08)
> John had been working on a context theory since the 1980s, and he had
> several students who developed versions. Guha was one of the first,
> with his PhD dissertation in 1991, which was also published as a Cyc
> technical report.
>
> At the end of the meeting, John explicitly said that it would be
> premature to standardize on any theory of context that had been
> proposed up to that point.
>
> I agree with him. But I believe that something like the 'that'
> operator is a prerequisite. (09)
The key point about the 'that' operator is, that it obviates the need to make
any fundamental change to the underlying logic. The basic logic of IKL is
simply first-order reasoning of the very same kind that has been used since
Peirce and Russell. Contrary to what JMcC and his students have claimed, one
does not need a context logic in order to logically formalize contexts. (010)
> There are many different ways of
> axiomatizing how you would use the 'that' operator to support
> a theory of context. (011)
Yes, exactly. For a lot more on this topic, see
http://www.ihmc.us/users/phayes/IKL/GUIDE/GUIDE.html#ContextsModalities (012)
Pat (013)
>
> John
>
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