Re: Principle of Orthogonal Design(B
Date: Wed, 6 Feb 2008 11:12:19 -0800 (PST)
Message-ID: <c8b884d0-cbe9-4a34-a982-372be6e6529d_at_q21g2000hsa.googlegroups.com>
On Feb 5, 3:50 pm, JOG <j..._at_cs.nott.ac.uk> wrote:
> On Feb 5, 9:06 pm, Marshall <marshall.spi..._at_gmail.com> wrote:
>
> > However, suppose we have a binary predicate P over
> > domain X and we want to assert it is reflexive? In predicate
> > logic we can use the same name twice and express this
> > very conveniently:
>
> > Ax in X: P(x,x)
>
> In my own work I prefer to view the input of the predicate as a set,
> given attributes are no longer ordered. So to state reflexivity I'd
> have:
>
> $B"O(Bx P( { a:x, b:x } )
>
> With the : notation just being a shorthand to represent an ordered
> pair.
Hmmm. Syntactically they are ordered pairs, yes; but the use of that term here worries me, because the syntactic elements are names not values. But maybe I am just being picky.
> In fact, if one considers the full enumeration of the binary
> predicate (denoted as S), one can state reflexivity as:
>
> $B"O(Bx { a:x, b:x } $B":(B S
>
> Which I find kind of neat - that sort of notation allows one to get
> completely set-theoretic on a data model ass.
Yeah, that's sort of the direction I want to go in.
But you've still got tuple-level constructs in there, which
I think we can do without. Let's see:
X(x) -- the domain
R is reflexive if the domain extended to a and b is a subset of R
X & x=a & x=b => R
Let's try another one. Symmetry in its positional expression:
Aa in X: Ab in X: R(a, b) -> R(b, a)
Bleah. We have to swap attribute names, which means a
pair of renames. Um ...
R & a=c & b=d | set(c, d) {} & c=b & d=a => R
I'm sure no one can read that except me. "R join a=c
join b=d inner-union with the empty relation of attributes
c and d join c=b join d=a is a subset of R."
That would be a *lot* easier with a rename/rebind
operation.
R => R(b,a)
I need to work on this sometime when I'm not stupid.
R(a, b) -- the relation
> Hmmm. I really must remember to use that terminology
> in a paper some time.
Yes you should.
Marshall Received on Wed Feb 06 2008 - 20:12:19 CET