I am relearning semantic web technologies and foundational mathematics. Currently, I am trying to understand the nature of whatever theory underpins RDFS: is it a set theory (and if so, what kind?), a type theory (likewise?), a description logic (ditto?), or something else?
The relations that hold in RDFS include the following:
rdfs:Classis a subclass of
rdfs:Resourceis a member of
rdfs:Classis a member of
- (4) the
rdf:typerelation "indicates that a resource is a member of a class"; and
- (5) the
rdfs:subClassOfrelation "specifies a subset/superset relation between classes".
See the upper-left nodes in this diagram from the RDFS specification:
If I understand correctly, then whatever theory underpins RDFS, it has the following properties:
- if it is a set theory, then it is non-well-founded, due to (3).
if it is a set theory, then, due to (5) it could be said to follow Set Theory and its Logic (Quine, 1969) in taking it to be the case that (pp.1-4, emphasis mine):
Sets are classes. ... Basically 'set' is a synonym of 'class' [because] the distinction [between sets (classes capable of being members) and 'proper classes' (classes not capable of being members)] emerges only in systems that admit [proper] classes, and even in such systems the classes we have to do with tend to be sets rather than [proper] classes until we get pretty far out.
My main question is: am I correct? If not, please explain the way in which I am mistaken.
My secondary question follows. RDFS has one standout elegance: its "property-centric approach ... allows anyone to extend the description of existing resources, one of the architectural principles of the [Semantic] Web." Beyond that, it seems to be a mongrel application of various theories. Perhaps there is an underlying consistency and elegance I am failing to notice, that falls under some cohesive heading. Is there a name for the branch of mathematical theory underpinning RDFS?