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## Re: [ontolog-forum] What words mean

 To: "[ontolog-forum] " Christopher Menzel Sat, 23 Feb 2008 17:25:34 -0600 <08453A03-3AA0-44BE-90FE-6867F05F7945@xxxxxxxx>
 ```On Feb 23, 2008, at 3:04 PM, Wacek Kusnierczyk wrote: > Christopher Menzel wrote: >> On Feb 23, 2008, at 9:19 AM, Wacek Kusnierczyk wrote: >> >>> ... >>> By definition (one from graph theory, Azamat might have had other >>> definitions in mind), a tree is a connected acyclic graph. >>> Undirected >>> trees have no roots. >>> >>> A rooted tree is a directed tree with exactly one distinguished >>> vertex >>> chosen as the tree's root. Following the definition (in a rooted >>> tree, there is exactly one path from the root to any other vertex in >>> the graph), if a tree were to have two roots, each of them would >>> have >>> to be accessible from the other, which implies a cycle in the graph; >>> but such a graph is not a tree. >> >> Yes, though one can define trees so that multiple roots are allowed, > > obviously, anyone can provide any definition one wishes for the term > 'tree', in any context.    (01) Well, that's just a *bit* disingenuous. Obviously, one could define "tree" as a synonym for, say, "partial ordering" or "continuous nowhere differentiable function". The point is that there *are* definitions of 'tree' in specific research communities that permit multiple roots, and there are contexts where it is convenient to do so.    (02) >> though of course in those cases the trees would not be connected; >> you'd have what by other definitions would be called a forest, as >> > yes; and since trees are connected graphs,    (03) In graph theory.    (04) > and forests are disconnected    (05) Except in the limiting case of a forest consisting of a single tree.    (06) > -- disconnected unions of trees -- no forest is a tree (though > admittedly i'd have a hard time saying that forests are not trees ;)). > you can call a forest a 'tree', but such switching names does not > change > the fact that what is referred to in graph theory by the term 'tree' > cannot have more than one root,    (07) Nor does this fine, if entirely obvious, expository point change the fact that in set theory a 'tree' *can* have more than one root. Look, I'm not claiming it's a good or bad idea. I was just making what I'd thought was a completely straightforward and uncontroversial point, viz., that there are in different contexts different (though obviously related) definitions of 'tree', and that, for *applied* purposes, you are free to choose the one that suits your purposes best. Obviously, if you are *working* in graph theory, you would not want to alter the conventional definition, but I didn't take that to be the context of Paola's question.    (08) > now, if paola was asking about graph-theoretic trees specifically, the > answer was clear. the answer is likely to be different if some other > meaning of 'tree' is considered.    (09) Of course. As noted, I didn't take her question to be specifically graph-theoretic.    (010) >> Randall noted. This is the case for the general set theoretic >> definition of a tree as a partially ordered set such that the set S_n >> of predecessors of any node is well-ordered by the partial ordering >> restricted to S_n. Not surprisingly, one often subsequently finds >> the >> definition of a "normal" tree among the conditions for being which >> are >> that the tree has only one root. >> > it is easy to imagine, in addition to trees and forests, graphs that > are > connected and appear, in some way, tree-like, with more than one > vertex > designated as a root. but they either contain cycles, or some of their > vertices are not reachable from one or more roots.    (011) Well, sure thing.    (012) -chris    (013) _________________________________________________________________ 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) ```
 Current Thread Re: [ontolog-forum] What words mean, (continued) Re: [ontolog-forum] What words mean, Randall R Schulz Re: [ontolog-forum] What words mean, Christopher Menzel Re: [ontolog-forum] What words mean, Sharma, Ravi Re: [ontolog-forum] What words mean, Christopher Menzel Re: [ontolog-forum] What words mean, Azamat Re: [ontolog-forum] What words mean, paola . dimaio Re: [ontolog-forum] What words mean, Wacek Kusnierczyk Re: [ontolog-forum] What words mean, paola . dimaio Re: [ontolog-forum] What words mean, Christopher Menzel Re: [ontolog-forum] What words mean, Wacek Kusnierczyk Re: [ontolog-forum] What words mean, Christopher Menzel <= Re: [ontolog-forum] What words mean, Wacek Kusnierczyk Re: [ontolog-forum] What words mean, John F. Sowa Re: [ontolog-forum] What words mean, Barker, Sean (UK) Re: [ontolog-forum] What words mean, Christopher Menzel Re: [ontolog-forum] What words mean, John F. Sowa Re: [ontolog-forum] What words mean, John F. Sowa Re: [ontolog-forum] What words mean, Azamat Re: [ontolog-forum] What words mean, John F. Sowa Re: [ontolog-forum] What words mean, Christopher Menzel Message not availableRe: [ontolog-forum] What words mean, paola . dimaio