Re: Interpretation of Relations

On 2007-01-23 12:23:37 +1000, "JOG" <jog_at_cs.nott.ac.uk> said:

> Joe Thurbon wrote:

>> [snip]
>>> Say we have a proposition from
>>> the real world, which has three roles x,y and z, and three
>>> corresponding values a,b and c.  RM as it stands would represent this
>>> proposition directly as a tuple:
>>> 
>>> P(x:a, y:b, z:c)
>>> 
>>> whereas I believe a tuple should perhaps  represent it 'indirectly' as
>>> a compound predicate:
>>> 
>>> Exists p x(p,a) ^ y(p,b) ^ z(p,b)
>>> 
>>> I believe the consequences of this subtle change in interpretation of
>>> what we are 'recording' (facts - or statements /about/ facts) _may_ be
>>> able to remove a lot of the logical errors generated by missing
>>> information, and perhaps some other issues too. But don't quote me on
>>> that.
>> 
>> I'm not sure exactly what the change in notation here is buying you.
>> The formula still looks like facts, rather than statements about facts.

I was a bit terse (I was trying to get a reply in before work) - I didn't mean to suggest that the approaches were equivalent. In fact, I think there is some real merit in the F2 approach (if I understand it).

One thing concerns me, though. Where do the 'p's come from? The only interpretation I can make of them are that they are the 'things' which the 'facts' are about. Or are you actually quantifying over predicates? (In which case you're using 2nd order logic).

> F1 comments
> about the real world directly, whereas in a sense F2 is commenting
> about F1 (especially given it starts with existential quantifier,
> 'there is a proposition').

In FOL, you don't quantify over propositions, you quantify over constants. So you are talking about 2nd order logic (which is fine, I just know close to nothing about it). At this point, I'm actually unsure how to read F2 above.

> It also incorporates attribute names
> explicitly within the encoding (which seems to correspond to Codd's
> move to 'relationships' between the 1969 and 1970 paper pretty well)
> and it reflects the unordered nature of attributes in databases, given
> the conjunctions are commutative.

Yes, I like this.

>
> Either way, I think it would be more than a change in notation - the
> database is no longer expected to comment reliably on the real world,
> but rather just on what we know about the real world. If it stores one
> fact "I have been given a proposition that states Joes hair is Red",
> CWA over the database no longer implies that Joes hair is not black,
> but rather just that "I have not been given a proposition that states
> Joes hair is Black", saving me from any missing information
> contradictions.

I understand the intent. I think your translation is on the right path, but I think it's not quite what you intend.

>
> As a logician perhaps you can tell me if the following makes any sense
> - to say Joe does have a hair colour and is not bald, I'd have:
> P = Ep Name(p, Joe) ^ Ey Hair(p, y).
>
> Or to say Joe is bald:
> P = Ep Name(p, Joe) ^ ~Ey Hair(p, y).
>
> Or to say I don't know if I don't know if Joe is bald or not, well this
> is inferred from not saying anything at all.

Yep, this makes sense to me. I'm assuming that by "=" you mean 'is defined as'. It's not really a part of FOL, that I'm aware of, but it makes sense.

Just to clarify what I was talking about above, in this situation, Joe and p are not propositions, though, they are a constant and a variable. So, to relate this to the relation

HasHair(Person:p, Hair:h)

you have to do something more than just have an Ep around. HasHair is not in the domain of the Exists.

>
> There are other possible consequences in terms of being able to more
> advanced collectivizing of propositions but I'm nowhere on top of it
> (having to pay a mortgage and all),

I hear you!

[...]

Cheers,
Joe Received on Tue Jan 23 2007 - 11:59:13 CET