Re: [ontolog-forum] Need advice

[William Frank <williamf.frank@xxxxxxxxx>]

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 and 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.'

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.

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.  

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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