- From: Bijan Parsia <bparsia@cs.man.ac.uk>
- Date: Wed, 2 Jul 2008 09:43:43 +0100
- To: OWL Working Group WG <public-owl-wg@w3.org>

Here's a analytic summary to help drive the discussion. First, I'm working with two users (Sebastian Brandt and Robert Stevens) to come up with some understandable but realistic example of (at first) linear equations used in TBoxes to drive subsumptions. There has been doubt expressed as to whether n-ary is a "really needed" feature (first by HP (withdrawn) and then by Boris (at the first f2f)) or whether some sort of rule mechanism would be better (though, even a standard DL-Safe rule mechanism would most likely require constraint reasoning). I intend for these examples to be runnable on the current version of RacerPro, so we'll be able to examine them in detail. I hope to get these working in the next week or so. Second, there are still open issues with the current proposals, some of them resting on the current datatype discussion. E.g., as with facets, we have to be careful to restrict the types of arguments to the equations we support to "sensible" types, or rather, how we handle nonsensical types. For example, we need to say something about what happens if the possible value of an argument to a polynomial is a string (or a double! or an integer!) (Nonsense can be driven by violations of user intutions, extreme difficulty of implementation, or fundamental theoretical problems (e.g., undecidability)). Third, expressivity: Let's consider numbers (and, indeed, reals) only for the moment. We can see the proposal as containing a hierarchy of more and more comprehensive support: 1) Syntactic hooks (what we have now) plus appropriate datatype (e.g., reals) Since we only have unary datatypes (>5) there's nothing we can actually do with the hooks. 2) Comparison operators only; that is, we can say (x>y). Now we can use the hooks, but we have no equations There are use cases for this 3) Linear (in)equations; e.g., x > 2y This suffices for many applications; some version of this is supported by the current release of RacerPro (and has been so for years). We allow rational constants but (algebraic) real solutions (with no way to force integer solutions). There are existing solvers which I believe could be fruitfully adapted (based on experience using them for probabilistic reasoning). They are able to handle rather large and complex systems of equations. 4) Polynomial (in)equations; e.g., x = y^2 + 3 This is still decidable (given the right restrictions). I have a version of RacerPro which supports these, but it's not the released one. The current proposal sketchily says that up through 3 is required and 4 mandatory. I do believe that 3 is a reasonable burden to spec and implement and will hammer out the various issues that arise. At least 3 is current supported by Racer and on the to do list for Pellet and FaCT++ (basically, they're waiting for a spec!). The intent for 3 is to allow for a fairly straightforward modular implementation where existing solvers can be plugged in. Fourth, syntax: The XML/functional syntax is easy, though we could add a bit of sugar to make writing equations nicer. I don't see any reason not to use MathML. For RDF, I thought equations could use MathML too (as a literal or data uri) for inline equations. We should also allow naming predicates. (The situation is pretty similar for strings. But I think this gives enough of the flavor of the situation for fruitful discussion.) Fifth, naming and conformance: Since datatypes and predicates are extensible, perhaps we should follow the DL conventions and have an extensible naming scheme. This would help implementations that wanted to support more modest data reasoning. Cheers, Bijan.

Received on Wednesday, 2 July 2008 08:44:16 UTC