<OR> predicate?

On 26/09/2010 4:11 PM, paul c wrote:
...
>
> ps:There might be occasional usefulness in making what one might call
> 'domain assertions', eg., in D&D Algebra, "there is a position called
> 'toilet scrubber'" could be assessed from R{position} <OR> (<NOT>
> R{position})...

That makes me think of a question that may not have any practical point except for understanding the 'A-algebra' (because it involves non-union-compatible relations).

Suppose the predicate of R{Position} is "position Position is occupied".

I would think one possible predicate of R <OR> (<NOT> R) would be something like "position Position is occupied OR unoccupied".

Seems that an even simpler expression, R <OR> TABLE_DEE, gives the same extension. Is the predicate the same? Or is there a good reason to think instead of the predicate as something like "position Position Exists"?

(I'm asking this question even though I personally have some difficulty reconciling parts of the A-algebra formal definitions, eg., on one hand, the heading of R <OR> TABLE_DEE must include the heading of TABLE_DEE which is the empty set (in other words, the empty set is a member/element of the heading and I presume being a member is not the same as being a subset). On the other hand, the definition of an A-algebra heading says that it is a set of ordered pairs. But the empty set is certainly not an ordered pair. I assume I must be making some mistake, otherwise R <OR> TABLE_DEE is not a valid expression. By 'valid' I mean theoretically possible. Maybe somebody can point out how I'm making this mistake.) Received on Mon Sep 27 2010 - 19:57:21 CEST