I take the point of the question to be that the world is in some sense uncertain (I'll expand on this later) yet the semantic web models are logic based with facts either being true or not. A resource is either a member of a given class or it is not. Surely to adequately represent many real world phenomena we'll eventually need to represent things which are not so discrete and aren't amenable to such simple logic-based classifications?
TBL's answer in the discussion was an interesting one, essentially it was that models of uncertainty won't scale to the web. If you consider a typical uncertainty representation in the form of a belief network (this could be Bayesian, Dempster-Shafer or almost anything for the moment), then to work out a belief value for some node you combine values from input nodes. To avoid double counting the contributions when the belief network is a graph, rather than a tree, you need to see the whole network. This doesn't scale to the web. In contrast logical assertions scale because you only need to see the conclusion, not all the paths which contributed, or could have contributed, to the conclusion.
That's a good answer but one which can be challenged, and we'll push on it a bit below.
Another answer that could have been given is that the nature of the semantic web that is currently envisioned is that of a large federated database, rather than that of a world-spanning knowledge representation system describing real-world phenomena. Databases are, pretty much by definition, symbolic things. You can store statistical data in them but apart from some rather specialist systems the databases themselves aren't probabilistic or fuzzy things.
A third answer, given by Jeremy Carroll, is that in practice for any given assertion on the web then you will probably find counter assertions elsewhere and the collective set of related assertions across the web might represent the community consensus on how much faith to put in any one variant of the assertion. In essence the web allows all sides of a given argument to be represented and, for a given application, a developer can chose which side to buy into.
Of course, you are not barred from representing statistical or belief-qualified data. You can always create an ontology to describe your favorite representation of belief or uncertainty and use that to encode any given statistical measures or belief network for transmission across the semantic web. The question is more whether such a representation should be built in at a fundamental level so that every semantic web agent should be expected to understand it.
Is the web-scaling argument water-tight? I don't think so. First, even if it were true it is "no excuse". If your data is fundamentally continuous or uncertain and you are forced to simplify it down to symbolic discrete assertions then you are introducing errors. The fact that those errors can now propagate globally without dilution is hardly a positive thing! Second, some uncertainty representations like fuzzy logic use non-linear combination functions which might scale (fuzzy logic uses min/max to combine values so repeat combination of the same information does not introduce errors, though the assignment of compatible fuzzy measures in the first place will have its own scaling challenges). Third the plan is that the semantic web will eventually need a proof trace layer so that the evidence for a logical deduction can be traced back so you can check the sources and the deduction path for correctness. If you are going to represent the deduction path anyway then that should be enough to handle the multiple-evidence path problem in many uncertainty calculi.
However, there is some strength in the scaling argument and, anyway, if you take the view that the semantic web is just a big database you probably don't need to worry about belief networks.
So why worry at all? Why not just accept that symbolic processing is enough for now and get on with it?
To get at this we need to pick apart this concept of uncertainty a little.
At the risk of grossly oversimplifying such an important area, I just want to distinguish two different forms of what we've loosely called uncertainty.
First, there is uncertainty in the sense of statistical phenomena. Either the world you are looking at is fundamentally statistical (with is true of everything at the quantum level but let's not go there) or the nature of your measurements introduce noise. I do think this is important, but not fundamental to the semantic web. It would be useful if there was an agreed best practice for how measurements are represented on the semantic web that included the ability to represent statistical distributions. However, that need not be a fundamental part of the semantic web standards - just a commonly used ontology or two, perhaps supported by the Semantic Web Best Practice working group.
Second, and more important for this discussion, is uncertainty in the sense that our simple symbolic models are only approximations of complex, continuous, non-partitionable real world concepts. Such approximations are only ever good enough in particular constrained contexts. Even fundamental seeming dichotomies like plant/animal or male/female are not rigid partitions of the world. For many uses an ontology that says that the concepts male and female are disjoint and that every being is one or the other is good enough. Yet in some cases we, for example, might need to separate the notions of physical and mental male/female orientation, neither of which are strictly disjoint.
Now the connectionists argue, with some merit, that much of the world is like that - complex and continuous - and that symbolic reasoning systems in general have failed. If the semantic web were about strong AI and representation of common sense knowledge that would be a serious worry, but it is not. So if the semantic web is just not straying into that territory why worry about the approximate nature of our conceptual models? Why do I care enough to write this long, and now somewhat rambling, blog dump?
Fundamentally because the semantic web is about finding connections.
If you have a closed system, like a web site, and happen to be able to use RDF under the hood to power it that's nice, and a good use of the standards and the tools, but doesn't really move us very much towards the semantic web vision. That vision calls for data to be exported and exposed in such a way that disparate data sets can be discovered and linked and the connected whole is greater than the sum of its parts. To find such connections when we aren't all using a shared global ontology we need to build in hooks that allow us to match up classes which are different approximations of the same concept. To me this means we need some notion of approximate class membership or relations to help us discover those connections.
For example, one could then link the terms (both classes and properties) in a specific ontology to other broad concept vocabularies like wordnet. The relation between your particular classes and the wordnet concepts might be quite approximate and you might need to combine several wordnet terms to give a guide to what your class is about. However, even if such a link didn't carry any semantics in the logic sense it would still be useful. In the absence of such information then for discovering links we are reduced to traditional schema matching techniques which combine string matching with some string-based term generalization (probably using wordnet!) with some structural matching. Explicitly documenting the nature of your modeling using some "approximately conceptualizes" link would give schema matching much more to bite on.
Some of this already goes on. In foaf, for example, the classes like Person are linked to wordnet concepts. This is a great start. It is not the full answer - it's not obvious that wordnet concepts can really be regarded as classes and the link may not really be a strict subclass link. For instance, if you create an ontology which includes concepts of male and female but they are not disjoint (to allow for hermaphrodites) then you can't use subclass to link to an upper ontology which regards those concepts as disjoint.
We have experienced this problem in practice. We were creating a personal profile ontology and wanted to link to and reuse existing ontologies like foaf, vcard, and the DRC-Orlando Person ontology. It was very hard to use sub-property to relate concepts like "name" because each has a different representation of name (different divisions into name components) yet somehow they are conceptually very similar and it would have need nice to be able to record that similarity.
Wrapping up. We may not need to build in an uncertainty representation in the sense of explicit degrees of belief (though a best practice solution for that would be useful). However, our models are crude approximations and we do need some way to link concepts which are not strictly logically related but are approximations of each other to help with connection discovery. A way of leaving better "breadcrumbs".