Expressing quantification as a binary relation

Aaron Swartz:

[...] I would like to see that special meaning represented using standard
triples, not a special representation in the abstract syntax. One example is
the log:forSome property use in CWM.

Seth:

I agree. I think RDF carries with it the assumption that all representations
can be reduced to BinaryRelations [1]  ... if this is not the case, then RDF
is in deep trouble.

[1]
http://ontology.teknowledge.com:8080/rsigma/SKB.jsp?req=SC&name=BinaryRelati
on

Pat Hayes:

The problem with this is that it then becomes impossible to provide a single
coherent model theory. log:forSome is a good example, in fact. If that means
what it apparently is supposed to mean, then any triple using it cannot be
interpreted according to the terms used in the RDF M&S, since the latter
claims that a triple indicates a relation holds between two things; but
log:forSome is a quantifier, which is not a relation. The intended meaning
breaks the earlier semantic model.

Seth:

I think quantification can be represented as a BinaryRelation between a
Boolean variable and a BinaryRelation.  As such it becomes the map between a
variable that binds to relations and a variable that binds to true or false.
Allowing this will allow us to represent quantification in as fine a detail
as we wish in our model and will get it out of the domain of just a
syntactic trick.

The KIF sentence:
(exists (?a ?b) (and ?a ?b))
would become something like:
(and (existTruthValue  ?a ?aBound) (existTruthValue  ?a ?aBound) )

I've gone into more detail in the mentograph [2]

[2] http://robustai.net/mentography/quantification.gif

For a semi complete presentation of mentograpy, the graphic notation of
BinaryRelations (labeled directed graphs), see [3].

[3] http://robustai.net/mentography/MentographySemenglish.gif

Seth Russell

Received on Tuesday, 10 July 2001 18:04:37 UTC