>John, PatH:
> I have been "loosely" using context as an argument in a
>"holdsInContext" relation, which gives propositions of the form:
> (holdsInContext ?Prop ?Context) (01)
Right, that's the McCarthy style of use, to speak
loosely. He and his followers write this as (02)
(ist ?context ?proposition) (03)
To do this as written requires that one has a way
to refer to a proposition, which is a big change
from conventional logics, which have no such
construction. We do this in IKL by reifying the
proposition as an object; there's a special IKL
construction for it: a term (actually a *name*)
of the form (04)
(that <text of sentence>) (05)
denotes a proposition which has the same
truth-conditions as that sentence (if there is
one). So one gets things like (06)
(holdsInContext (that (exists (x)(Loves John x))) DreamOnContext) (07)
> . . . and a proposition that holds in one context does not
>necessarily hold in another. (08)
Quite, that is the point. (09)
>
> This is somewhat off the topic of whether an identifier means the same
>thing in different contexts (I prefer that they do, and use
>context/namespace prefixes to address clashes). (010)
Yes. IKL adopts this position, as does Cyc.
Others however - and John is one of them -
maintain that this loses much of the
expressiveness of contextual logics. (011)
>But I am very concerned about what can be stated about the preservation
>of truth between contexts. (012)
What are your concerns, exactly? (013)
>For example, if a "context" is a time interval in the real world, what
>is true in one time interval may not be true in another. However, some
>things tend to remain true for long periods of time, such as the
>location of Mount Rushmore; and other things tend to remain true in
>every spatial context (e.g. the number of protons in an oxygen
>nucleus). Has there been any discussion of how to address
>cross-context preservation of truth in a formal manner? (014)
Well, yes. There is lots written about this in
temporal logics. If one insists (sigh) on viewing
temporal reasoning as having to do with 'temporal
contexts', then all that can be applied directly
to context reasoning, providing of course that
one is talking about the right kind of context. (015)
The simplest way to talk about this seems to be
to have theory of subconexts, or of contexts
(read timeintervals) being contained in one
another, since obviously if something is true
throughout one interval it is also true during
its subintervals. Then this issue becomes
subsumed by a topology or mereology of contexts,
or whatever your theory thinks is the appropriate
structure on the space of contexts. I just wrote
a little paper on this for the AAAI Spring
Sympoium, take a look (016)
http://www.ihmc.us:16080/users/phayes/context/ContextMereology.html (017)
This only deals with the propositional case.
Quantifiers are more delicate because there are
different conventions for their use relative to
contexts (see above). There are some notes on the
topic in (018)
http://www.ihmc.us:16080/users/phayes/IKL/GUIDE/GUIDE.html#ContextsModalities (019)
Pat (020)
>
>Pat
>
>
>Patrick Cassidy
>CNTR-MITRE
>260 Industrial Way West
>Eatontown NJ 07724
>Eatontown: 732-578-6340
>Cell: 908-565-4053
>pcassidy@xxxxxxxxx
>
>
>> -----Original Message-----
>> From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx
>> [mailto:ontolog-forum-bounces@xxxxxxxxxxxxxxxx] On Behalf Of
>> John F. Sowa
>> Sent: Monday, April 16, 2007 10:41 PM
>> To: [ontolog-forum]
>> Subject: Re: [ontolog-forum] Ontology,Information Models and
>> the 'Real World'
>>
>> Pat,
>>
>> I sympathize with your attitude toward much of the loose talk
>> about contexts:
>>
>> > ... But in normal assertional logic, the quantifiers are the
>> > only such name-binding operators. Of course all these languages
>> > can be rendered down into functors applied to a single binder,
>> > usually lambda.
>>
>> I'm happy with that.
>>
>> > BUt contexts in context logic play a rather different role: in
> > > particular, there is no explicit name binding syntax, only
>> the notion
>> > that a name may (or may not) denote differently when asserted
>> > relative to a context. Contextual assertion is more like inclusion
>> > inside a modal operator than being in a syntactic binding scope.
>>
>> I prefer very simple formal definitions: a "concept" is a node
>> in a conceptual graph, and a "context" is a box into which you put
>> such graphs.
>>
>> They way I represent talk about a dog or a flea or the kitchen sink
>> as a context is straightforward:
>>
>> 1. I use the binding mechanism (such as the existential quantifier)
>> to represent the thing that is called a context (dog, flea, or
>> sink) by a variable x.
>>
>> 2. Then I use the "that" operator of IKL to represent the context
>> box and its nested CGs as a proposition p.
>>
>> 3. Finally, I use a *description* relation (Dscr) to link #1 and
>> #2 by Dscr(x,p).
>>
>> I have never seen any theory of contexts with a coherent set of
>> axioms that cannot be represented (with a considerable increase
>> in clarity) by restating the axioms by the above method (possibly
>> with some additional relations and types, such as Situation or
>World).
>>
>> John
>>
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