On Dec 12, 2014, at 9:08 PM, William Frank <williamf.frank@xxxxxxxxx> wrote: (01)
> Yup, inverse is more common in broader contexts, from which I think that OWL
>etc. get their usage.
>
> For example, in traditional linquistics, tthe relations father of ad son of,
>buyer, seller, are called 'inverse.' This sort of follows the terminology of
>logic, in which the inverse of 'if p then q' is i'f q then p.' (02)
No, this is the converse. The inverse of 'if p then q' is 'if not p then not
q'. See
http://hotmath.com/hotmath_help/topics/converse-inverse-contrapositive.html (03)
But in any case, the direction of an implication, on the one hand, and the
ordering of two arguments of a relation, on the other, really have nothing much
to do with one another. The inverse relation of a binary relation R is (lambda
(x,y) R(y,x)). (04)
> similarly, in function theory, the inverse of a function from domain D to
>range R is the other way around, the equivelent mapping back from Domain R to
>range D, which might not be a function, of course.
>
> I would vote to follow these traditions and say inverse. (05)
I agree. (06)
> While there is always an equivelent relation in the inverse direction for a
>function, this is something that has to be discovered, and in some languages,
>their will only be, for some so I do not think it is a good practice to
>dismiss the distinction as two ways of saying the very same thing. There
>could be interesting things about the language hidden in the fact that
>sometimes there are two ways of saying it, sometimes only one. And, of
>course, sometimes there is a navigatibility build into the situation.
>
>
> But both will work, because while
>
> the logical converse of 'if p then q' is 'if not p then not q,' this is
>equivelent to the inverse, 'if q then p,' so inverse and converse are
>logically equivelent. (07)
Indeed. (08)
Pat Hayes (09)
>
>
>
>
>
>
> On Fri, Dec 12, 2014 at 6:01 PM, Duane Nickull <duane.nickull@xxxxxxxxx>
>wrote:
> What would be a suitable term to call a binary relationship that is
>co-dependent yet not symmetrical to another relationship between the same
>entity in a binary relationship?
>
> If "John is a father of Chris”, how can we describe that relationship in
>terms of comparing it to “Chris is a son of John”? Would “isomorphic” be the
>best term to use? “Inverse”? Assume that the relationship is traversable from
>either side.
>
> The context of this is in a graph database discussion group. Graph Databases
>have nodes and relationships. Either can have properties. Unlike RDBMS
>systems, graph databases have relationships between instances of nodes, not a
>foreign key relationship with an entire table.
>
> The binary relationship is not symmetric since true symmetry would require
>that the statements “..is a father of…” and “…is a son of…” be equally true
>for A-B as they are for B-A.
>
> Sorry for this simple request. I am just trying to find the best description
>for this.
>
> Duane Nickull
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> www.hottomali.com
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