Re: Interpretation of Relations

From: JOG <jog_at_cs.nott.ac.uk>
Date: 21 Jan 2007 16:46:47 -0800
Message-ID: <1169426807.129352.191440_at_11g2000cwr.googlegroups.com>

Joe Thurbon wrote:
> [snip]
> Informally, it boils down to: if a database should be considered as a
> set of logical assertions, then you have to be very careful how you
> treat missing information, especially in the presence of the CWA. In
> facts the particular logic in which the facts are being asserted in is
> a modal logic.
>
> In particular, there are two types of relations,
> - those which should be interpreted as 'facts about the world', which
> can't really handle missing information, because of the CWA, and
> - those which should be interpreted as 'facts about my knowledge of the
> world' which can handle missing information.

This is extremely close to my line of research. As such this seems like a good opportunity to dig out something very similar, that started my line of thought in this direction. I had been attempting to look at the consequences of different encoding strategies for stating NL sentences as formal propositions, and the effects that the choices made have on the issue of missing information within the resulting data model. In the course of this I produced the following simple example of the effects of CWA and missing information that concerned me (I have reworked the example to correspond to the OP).

• Consider the dual predicates Joes_hair(x) and Not_Joes_hair(x), and an RM representation of them with a trivial domain:

Domain D_Hair = {Red}
Relation R_Joes_Hair = <value: D_Hair>
Relation R_Not_Joes_Hair = <value: D_Hair>

• Constraints: C1 = FORALL x R_Joes_hair(x) <-> ~R_Not_Joes_hair(x) C2 = FORALL x R_Not_Joes_hair(x) <-> ~R_Joes_hair(x)
• We obviously know from our encoding that: R_Joes_hair(value : x) -> Joes_hair(x) R_Joes_hair(value : x) -> Not_Joes_hair(x)
• Also, by the CWA we know that: ~ R_Joes_hair(value : x) -> ~Joes_hair(x) ~ R_Not_Joes_hair(value : x) -> ~Not_Joes_hair(x)
• Now, if Joe's hair is red one should encode: R_Joes_Hair = { (value:Red) } R_Not_Joes_Hair = { }
• Or if he does not have red hair one encodes: R_Joes_Hair = { } R_Not_Joes_Hair = { (value:Red) }
• However, I don't know Joe, so this information is missing, and this puts me in rather a spot. I cannot state R_Joes_Hair(Red) or R_Not_Joes_Hair(Red) because: Joes_Hair(Red) = UNKNOWN Not_Joes_Hair(Red) = UNKNOWN
• But worse still, if I do nothing at all and insert no tuples I have: R_Joes_Hair = { } R_Not_Joes_Hair = { }
• From CWA from this we could infer: ~Joes_hair(Red) ^ ~Not_Joes_Hair(Red) => ~Joes_hair(Red) ^ Joes_Hair(Red) => CONTRADICTION

This frustrated me somewhat when I first jotted it down, and even if it is missing a trick, it has given me some useful insights into how the issue might be addressed through a description of 'facts /about/ our knowledge of the world' (as you put it) via a SOL formalization - I'm not sure that modal logic is necessary in the db-algebra itself. However I am a long way from being a logician and as such have a healthy skepticism of the validity of absolutely any maths I generate, so any critical analysis is /more/ than welcome.

>
> I must confess, though, that I've not really read widely enough to know
> if this is a new take on RA. But perhaps someone here can let me know.
>
> Cheers,
> Joe
Received on Mon Jan 22 2007 - 01:46:47 CET