Pat Hayes wrote:
>> John, PatH:
>> I have been "loosely" using context as an argument in a
>> "holdsInContext" relation, which gives propositions of the form:
>> (holdsInContext ?Prop ?Context)
> Right, that's the McCarthy style of use, to speak
> loosely. He and his followers write this as
> (ist ?context ?proposition)
> 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
> (that <text of sentence>)
> denotes a proposition which has the same
> truth-conditions as that sentence (if there is
> one). So one gets things like
> (holdsInContext (that (exists (x)(Loves John x))) DreamOnContext)
>> . . . and a proposition that holds in one context does not
>> necessarily hold in another.
> Quite, that is the point.
>> 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).
> 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.
>> But I am very concerned about what can be stated about the preservation
>> of truth between contexts.
> What are your concerns, exactly?
>> 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?
> 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.
> 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. (01)
I protest (weakly, since I may have misunderstood you).
An example: it is true throughout the whole century -- i.e., at any
time instant within the century -- that the sum of distances between an
instant and the beginning and the end of the century equals 100 years.
This does not hold for any proper subinterval of the century. (02)
I agree that this example is extreme and silly, and it is based on the
assumption that there are time instants, not just intervals. (03)
> 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
> 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
>> Patrick Cassidy
>> 260 Industrial Way West
>> Eatontown NJ 07724
>> Eatontown: 732-578-6340
>> Cell: 908-565-4053
>>> -----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'
>>> 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
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Wacek Kusnierczyk (06)
Department of Information and Computer Science (IDI)
Norwegian University of Science and Technology (NTNU)
Sem Saelandsv. 7-9
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