Re: recursive "shapes" in Description Logic literature

Peter,

Thx for the references. I am not sure the situation we have with
constraints is exactly the same as with defining terms. There is a
similarity between terms and shape labels. However, with shape labels
we have a split into two kinds of information.

The first kind deals with the constraints that are defined without
reference to other shape labels, e.g. cardinality, allowed values.
These cause no difficulty.

The second kind refers to other shape labels, e.g. that the object of
certain kinds of triple must have a certain shape (or in the case of
negation, must not have that shape). These may cause difficulty in the
presence of cycles.

I believe we can define a sensible and intuitive semantics if respect
this split.
Conceptually, we evaluate the graph in two passes. Pass one applies
the second kind of constraint to determine which shapes should hold or
not hold at each node. This is what I called a labelling and what
Iovka calls a typing, although her typing mixes value and shape
constraints. Pass two takes the labelling and for each node and shape
label in the labelling at the node evaluates the first kind of
constraint.

I'm still working through Iovka's spec. Not sure if I can actually
split her definition of valid typing into two passes.

-- Arthur

On Fri, Jul 10, 2015 at 1:39 AM, Peter F. Patel-Schneider
<pfpschneider@gmail.com> wrote:
> In the teleconference today I mentioned that there is literature relevant to
> recursive shapes in the Description Logic literature.
>
> The first major paper in this area is Terminological Cycles: Semantics and
> Computational Properties by Bernhard Nebel, available at
> citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.49.6816&rep=rep1&type=pdf
>
> Another relevant paper is Terminological Cycles in a Description Logic with
> Existential Restrictions by Franz Baader, available at
> www.ijcai.org/Past%20Proceedings/IJCAI-2003/PDF/048.pdf
>
> peter
>

Received on Thursday, 16 July 2015 17:50:49 UTC