A few comments.
1. I think you could add some more background to taxa as sets. You can't really not mention Gregg, see http://iphylo.blogspot.co.uk/2009/10/wikipedia-and-gregg-paradox.html Gregg championed taxa as sets defined by extension (i.e., enumerate all the member sof the set).
2. Should also mention work by Jessie Kennedy, Roger Hyam, et al. e.g. "The Prometheus Taxonomic Model: A Practical Approach to Representing Multiple Classifications" http://dx.doi.org/10.2307/1223932 They are advocating basically the same thing.
3. I'd argue that we already have taxa defined explicitly as sets, in databases such as BOLD (for any BIN we can list all specimens assigned to that BIN), GenBank (a taxon is a set of sequences), and GBIF (we can list all occurrences assigned to a taxon). For DNA barcoding, at least, there is also an explicit process for assigning specimens to taxa, so we basically have what you are advocating.
3. I'd avoid any suggestion that species as sets has anything to do with relational databases. All the cool kids are using NoSQL and graph databases, which also lend themselves very well to these problems. There's no necessary link between what you're doing and relational databases.
4. Might be worth mentioning that in a system like this we could do the inverse query, namely what is the history of taxonomic assignment of a specimen? For example, when we sequence a type and discover it's the juvenile of an already described species.
5. Really needs some actual, real examples. One of the reasons I like graph databases is that you can construct "live" examples that people can play with and explore (e.g., Neo4J gists). Even if that's not the databasse technology used, it can make things clearer.
A few typos scattered around.
Not sure what you mean by "primary type" here. If a set has more than one type, they are still all types because types go with names, not taxa. We apply rules to find out which type gives it's name to the taxon (usually the one with the oldest published name). Taxa don't have types, names do.
3.2 Consistency of species concepts
There are parallels here with character compatibility (which is about compatibility of partitions or "splits"), and also "open world" versus "closed world" assumptions (a la Semantic Web) (e.g., whether or not you can assume that a taxonomist has looked at all specimens at time t and made statements about all of them). This is a bit like character compatibility with missing data. I'm trying to remember whether there are cases where you can have characters that are compatible if you ignore missing data, but any possible resolution of the missing data woud make them incompatible. If this is the case, then it has implications for your approach.
Primary types as starting point
NCBI are very interested in sequencing types (the ultimate "digitisation") so might be worth linking to them (Scot Federehn has some papers on this).
Hope this helps.