Re: recursive "shapes" in Description Logic literature

I don't see that there should be any conceptual distinction between
constraints that are defined without reference to other shape labels and
constraints that refer to other shape labels.  These are both just constraints.

It is certainly true that constraints that refer to other shape labels
introduce difficulties in both the semantics and in implementation.  One way
around the semantic difficulties is to introduce the separate notion of an
interpretation (or labelling if you prefer), as in many logics including
Description Logics.   Interpretations are then validated as models.  One can
also have preferences, which again have quite a history in logic, and have
been considered in Description Logics.

peter

On 07/16/2015 10:50 AM, Arthur Ryman wrote:
> 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 20:07:40 UTC