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## Re: [ontolog-forum] Thing and Class

 To: "'[ontolog-forum] '" Matthew West Sat, 13 Sep 2008 13:43:15 +0100 <48cbb5cf.0c92100a.3e0c.5b9c@xxxxxxxxxxxxx>
 ```Dear John,    (01) It is good to see that we seem to be coming closer together again.    (02) > > MW> The real difference is that 3D sees that what exists now is all > > that exists, whilst 4D sees the past and the future as part of > > what exists as well as the present. This is what it means to stand > > outside time. > > I agree with that description, but you seemed to suggest that the > notion of change does not exist in a 4-d view, but I think that > we were using different definitions of 'change'.    (03) [MW] Yes, to try to draw an analogy, a 3D view might see a point changing its position over time, whereas in 4D you would see a line that appears static but is extended in time. > > MW>> all spatio-temporal extents exist (at all times, but > >> strictly independent of time). > > PH> Agreed, and a nice analysis. Putting the same point in logical > > terms, the universe of discourse shouldn't be in a state of flux, > > I have no quarrel with that, but it has nothing to do with the > definition of the concept of change. According to the most common > definition, if time slices at t=0 and t=1 are identical, there is > no change.    (04) [MW] That is a useful way to make 3-4 D neutral definition of change. > > Another way to say it: if the partial derivative with respect > to the time coordinate is 0, there is no change; otherwise, there > is change in that region of space-time. The existence of change > does not imply that the global 4-d universe is in flux. It just > means that there is some region in the universe where the derivative > with respect to time is not zero.    (05) [MW] Agreed. > > MW>> And interestingly, I again use possible worlds as an alternative > >> to modal logic. Not that I object to others using modal logic, but > >> I do not see that I am obliged inevitably to do so. > > PH> Again, I agree that this is the best approach. I think this is > > widely accepted, by the way: John McCarthy made the same point many > > years ago : > > http://www-formal.stanford.edu/jmc/modality/modality.html > > I believe that what John McC, Matthew, and Pat are recommending is > very close to Dunn's semantics for modal logic.    (06) [MW] I have always assumed this, but of course I prefer not to use modal logic. > > Most AI work with "possible worlds" is actually based on metalevel > reasoning about sets of propositions that describe those worlds, > not with the worlds themselves.    (07) [MW] Actually, I am more interested in populating those worlds with actual plans, than I am with reasoning, and then tracking how well they match to reality.    (08) > Starting with any Kripke model > K=(W,R,Phi), where W is the set of words, R is the accessibility > relation among worlds, and Phi is the evaluation function, those > sets can be derived: > > 1. For each word w in W, define the facts of w as the set of all > propositions p that are true in w: {p | Phi(w,p) = True}. > > 2. Define the laws of w as the set of all propositions p that are > necessarily true; i.e., p is true in all worlds accessible from w. > > 3. Define the accessibility relation R(w, w') as True iff every > proposition p that is necessarily true in w is also true in w'. > > This construction replaces every world in a Kripke model with a set > of laws and facts in a Dunn-style model. Any theorem that can be > proved about a Kripke model is also true of the corresponding Dunn > model. But Dunn's version is more *usable* because it makes the > laws and facts available for further analysis and manipulation.    (09) [MW] I have of course heard this before, and have not found anything obviously objectionable, but I would be concerned if this involved modal logic. > > PH> John's way follows Dunn's theory and is based on intensional > > descriptions. The far more commonly used view uses Kripke's > > possible-worlds account of modalities. Kripke's is widely accepted > > as the standard, and certainly gives a more usable semantics... > > Not true. Nobody actually implements "possible worlds".    (010) [MW] What do you mean by this? For example, I expect to have an object that represents a particular possible world (well more properly a universe) for all the time that it exists, and then to have objects in the world as spatio-temporal parts of it. How does this fit with what you mean?    (011) Regards    (012) Matthew West http://www.matthew-west.org.uk/    (013) > What they > implement and reason with and about are sets of statements of the > laws and facts of those worlds. Since the above construction can > map any Kripke model into such sets, most people who implement such > systems pay lip service to Kripke's version, but they actually use > something that is much closer to Dunn's version. > > For further discussion of these and related issues, see > > http://www.jfsowa.com/pubs/laws.htm > Laws, Facts, and Contexts > > http://www.jfsowa.com/pubs/worlds.pdf > Worlds, Models, and Descriptions > > John > > > _________________________________________________________________ > Message Archives: http://ontolog.cim3.net/forum/ontolog-forum/ > Subscribe/Config: http://ontolog.cim3.net/mailman/listinfo/ontolog- > forum/ > Unsubscribe: mailto:ontolog-forum-leave@xxxxxxxxxxxxxxxx > Shared Files: http://ontolog.cim3.net/file/ > Community Wiki: http://ontolog.cim3.net/wiki/ > To Post: mailto:ontolog-forum@xxxxxxxxxxxxxxxx >    (014) _________________________________________________________________ Message Archives: http://ontolog.cim3.net/forum/ontolog-forum/ Subscribe/Config: http://ontolog.cim3.net/mailman/listinfo/ontolog-forum/ Unsubscribe: mailto:ontolog-forum-leave@xxxxxxxxxxxxxxxx Shared Files: http://ontolog.cim3.net/file/ Community Wiki: http://ontolog.cim3.net/wiki/ To Post: mailto:ontolog-forum@xxxxxxxxxxxxxxxx    (015) ```
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