On Jul 23, 2012, at 4:24 PM, doug foxvog wrote: (01)
> On Sat, July 14, 2012 02:03, Pat Hayes wrote:
>> (Sorry Ive been off-email for a while.)
>
> So have i.
>
>> On Jul 11, 2012, at 3:16 PM, John F Sowa wrote:
>>> On 7/11/2012 3:13 PM, Pat Hayes wrote:
>>>> They are not context *logics*. There is no provision in CL
>>>> for the referent of any name to vary with contexts.
>
>>> What?!?!?!?
>
>>> Where did you get requirement?
>
>> Not sure I understand your question here. What I said is simply true of CL
>> and IKL, as is obvious from their semantic rules.
>
> Are you merely claiming that there is no inter-context reasoning in CL and
> IKL, since there is no standard method of defining contexts? (02)
CL simply has no contexts in it anywhere. Contexts are not mentioned in the
metatheory, play no role in the syntax or the semantics. You might as well as
whether CL has inter-aardvarkian reasoning. 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 proposotions (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*. (03)
>
> That would mean that if someone wished to incorporate information from
> isolated knowledge bases, they would automatically be merged. (04)
If you "incorporate" two pieces of CL or IKL, what you get is their Boolean
conjunction. I guess you could call this "merging", yes. (05)
> For
> example, if Allstate merged a knowledge base of its customers in
> Texas in 1997 with one of new customers in Maryland, in 2012, its algorithms
> upon finding a statement from the 1997 kb that a driver was 18 years old,
> would charge the customer returning to the company in 2012 the rate for
> teenage drivers, since the context of the driver's age was lost. And it
> would generate an error on an assertion that the driver had been accident-
> free for 23 years. I would hope not . (06)
Me neither, but then I would hope that the information had not been coded into
CL or IKL without any reference to the transaction or valid dates and times of
the relevant data. (07)
>
>>> For example, many logicians recommend that proper names in
>>> natural languages be mapped to monadic relations in logic
>>> rather than individual constants.
>
>>> The name Aristotle, for example, would be true of the ancient
>>> philosopher, and it would also be true of the second husband
>>> of Jackie Bouvier.
>
>>> If you want a theory in which names can vary with contexts,
>>> then you can map each name in any NL to a dyadic relation
>>> instead of a monadic relation. The relation Aristotle(X,c),
>>> for example, would be true iff the individual X had the
>>> word 'Aristotle' as name in context c.
>
>> Not quite. You have to associate the name (not the individual) with the
>> context.
>
> I thought you didn't accept contexts. (08)
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.) (09)
>> In IKL you can treat a character string as a function, which
>> handles this very nicely. We did this for the IKRIS project mappings, you
>> may recall. There is an extended example involving Lacrosse in
>> http://www.slideshare.net/PatHayes/ikl-survey (slides 21- 23) showing how
>> elegantly it works. [For readers who think that the axioms shown there
>> seem complicated, I invite you to try to formalize this example using any
>> other notation of your choice.]
>
>> But notice, none of this changes what names themselves refer to.
>> ('Aristotle' c) refers to whatever the strong "Aristotle" refers to in
>> context c, but that does not change what the actual name Aristotle refers
>> to. IKL is a referentially transparent language throughout.
>
> Are you distinguishing "Aristotle" and "the actual name Aristotle"?
>
> Is one refering to a string, and the other to a constant in the KB? (010)
I am distinguishing Aristotle, whose name is "Aristotle", from whatever that
string (ie the string "Aristotle") might denote in a different context. In IKL
the latter could be expressed as a term of the form ("Aristotle" context)
which might refer to something other than Aristotle. But in all this IKL, each
expression denotes one thingo in a context-free way, ie no denotations *in the
logic* depend upon context. (011)
>
>>>> One could of course do whatever one chooses, but if the context
>>>> is supposed to modify or help determine what URIs refer to, then
>>>> treating a graph as such a context is explicitly prohibited by
>>>> the RDF specification documents. So this would not be legal,
>>>> conformant, RDF.
>
>>> The conventions of RDF, OWL, and URIs are totally independent
>>> of this discussion.
>
>> The comment you cited here was made in response to a claim by Doug
>> Foxvog, that an RDF graph could be considered to be a context,
>> which is why I referred to RDF.
>
> The RDF comment meant that within the graph a substatement is true,
> but it is not necessarily true without the surrounding statements. (012)
Nope, sorry, that is not how RDF works. Read the RDF specs! (013)
> For
> example, it may be true that (IF A THEN B), but that does not mean
> that A is necessarily true, even if it is stated as an RDF triple. (014)
You can't state a conditional as an RDF triple. (015)
>
>>> Any theory of contexts proposed by any
>>> philosopher or linguist could be mapped to IKL in one way or
>>> another.
>
>> Maybe. IKL seems to be one of the most expressive first-order languages I
>> have ever seen, but I wouldn't make such a large claim about it without
>> some evidence.
>
> Consider Cyc's microtheories. They are the sorts of contexts which i
> was referring to. (016)
Me too. IKL is actually *very* similar to CYCL, the underlying logic of Cyc. It
may even be identical to it: Doug and I have a plan to check this out in detail
one day. (017)
> The assertions inside can be mapped to B
> (AND B1 B2 B3 ...)
> while the defining assertions of the context can be mapped to A:
> (AND A1 A2 A3 ...)
> [Converting this to masses of triples is an exercise for the reader.] 8)#
>
>>> But the notations of RDF and OWL are far less expressive. I couldn't
>>> imagine anyone using them to reason about context logic.
>
>> I could :-) .
>
> You've got a good imagination. 8)# (018)
Actually its quite straightforward. Think of OWL importing as being like CYC's
linking of a context to a supercontext, apply it all to RDF, and take it from
there. Of course you don't get IKL or Cycl, but you do get something that has
many of their advantages over basic GOFOL when compared to current RDF. (019)
>
>> In fact I have explicitly suggested modifying RDF as a
>> context logic to the RDF WG, but I don't hold out a great deal of hope
>> that they will be willing to go along with the idea.
>
> Why not a unary Turing Machine? 8)#
>
> -- doug
>
>> Pat
>
>>> Perhaps
>>> one might represent the final conclusion of some deduction in RDF,
>>> but that doesn't impose any requirements on RDF.
>
>>> John
>
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>
>
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