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| From: | york earwaker <yorkearwaker@xxxxxxxxx> |
| Date: | Fri, 18 Jan 2008 01:46:25 -0800 (PST) |
| Message-id: | <802538.55212.qm@xxxxxxxxxxxxxxxxxxxxxxxxxxx> |
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Hi Patric, Always been a bit confused as to use of Orthogonal in different contexts. :-) In this case I guessing you mean, from the context of your message below, that which can be found in Wikipedia: http://en.wikipedia.org/wiki/Orthogonal#Taxonomy "Taxonomy In taxonomy, an orthogonal classification is one in which no item is a member of more than one group, that is, the classifications are mutually exclusive." I like your reasoning here and that of John's in a previous response to this topic. The idea of contexts as distinct and/or overlapping (non-orthogonal) sets. In fact the set of all contextual sets would be all possible places in time and space. Further each set would relative (Einstein) to the perspective of the observer. Which implies sentience and consciousness as prerequisites to context. To be useful though a sub set of all possible contextual sets would be useful. Starting from the perspective of Humans in the 21st Century on Earth. Then subdivided into useful perspectives, in Europe, Western Europe, England, London, City of London, Deutsche Bank, Credits and Derivatives, ... to which corresponding ontologies can then be built/derived/mapped. All the best,
York.
----- Original Message ----
From: Patrick Cassidy <pat@xxxxxxxxx> To: [ontolog-forum] <ontolog-forum@xxxxxxxxxxxxxxxx> Sent: Friday, 18 January, 2008 6:22:04 AM Subject: Re: [ontolog-forum] Scheduling a Discussion [was: CL, CG, IKL and the relationship between symbols in the logical "universe of discourse" and individuals in the "real world"] PatH, Concerning the question of whether “everything” is a context:
[PatH Ø Heres my point, let me illustrate it with a parable. Joe comes along and says, we need to discuss foodles. Its important to have a general theory of foodles. And I say, hmm, what are foodles? And Joe says, everything is a foodle.
Ø At this point, I conclude that what Joe wants is impossible, because there isn't anything useful to be said that applies to everything. Anything non-trivial will be true of some things and false of others: it will divide the universe into examples and non-examples. It will be a category.
I use “context” solely, as John Sowa does, as a syntactic device to circumscribe the applicability of assertions. As Amanda Vizedom describes for Cyc, it is more of a device to avoid unintended contradictions than to enable any special kind of “context reasoning”.
(1) Is there any “axiom” that applies to all contexts? (simplified for brevity: C1 and C2 differ)
(forall (?c1 ?c2 ?Prop) (and (not (implies (ist ?c1 ?Prop) (ist ?c2 ?Prop))) (implies (ist ?c1 ?Prop) (not (not (ist ?c1 ?Prop))))))
That is, (a) no assertion in any context absolutely guarantees that the assertion will be true in any other context. (b) A context is that (whatever) in which the principle of non-contradiction holds.
One can, however, define some probabilistic assertions, especially with respect to time intervals (as with differential equations) that assert the likelihood of some proposition in some time interval depends on its truth value in another time interval. As you emphasize, I agree that such reasoning is best done with specialized time-dependent logic (or calculations).
(2) Is “everything” a context? Although I have not asserted a “disjoint” relation between Context and anything else, I would be willing if pressed to declare that “PhysicalObject” and “AttributeValue” are disjoint from “Context”. Therefore, not everything is a context. It just doesn’t seem particularly useful to declare limits on what can be a context. I haven’t seen a list of context types that exceeds two dozen. Perhaps you have a larger list of things that have been considered as contexts? (I am assuming that the Cyc 6000 or so microtheories are combinations of their basic 12 dimensions)
The reason that I find contexts convenient as a syntactic device is that specifying a class for the first argument of the “ist’ relation allow me to create *combinations* of basic contexts (time, space, possible world, theory) so that I can assert things like “In the sci-fi story ‘Frabits’, Jack had a theory that said that the Earth in 1990 passed through a zone of the galaxy that changes the gravitational constant” “In the Sherlock Holmes mysteries, 221B Baker Street in London was the residence of the famous detective in 1888.”
Each instance of the class “Context” then would have specific (possibly unspecified) values for each of the separate (not necessarily orthogonal) dimensions of Context, such as time, place, possible world/fiction/realworld, theory, etc. Most interesting is the real world of course, but plans have to consider possible worlds.
Now, you may not find it interesting to allow for context combinations, but it hasn’t been clear what term you would use to label the class of entities that occur in the first argument of “ist”. If you think that “Context” causes hopeless confusion, please suggest another term that doesn’t cause even more confusion.
PatC
Patrick Cassidy MICRA, Inc. 908-561-3416 cell: 908-565-4053 pat@xxxxxxxxx
From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx [mailto:ontolog-forum-bounces@xxxxxxxxxxxxxxxx] On Behalf Of Pat Hayes
At 4:32 PM -0500 1/16/08, Deborah MacPherson wrote:
Not sure I understand the question. The identification of a category is what a definition does. The category in question is "context".
Heres my point, let me illustrate it with a parable. Joe comes along and says, we need to discuss foodles. Its important to have a general theory of foodles. And I say, hmm, what are foodles? And Joe says, everything is a foodle.
At this point, I conclude that what Joe wants is impossible, because there isn't anything useful to be said that applies to everything. Anything non-trivial will be true of some things and false of others: it will divide the universe into examples and non-examples. It will be a category.
Do you see the point?
Pat
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