[SCL] the relational component of an SCL interpetation

[Robert E. Kent]

I have a question that may be just a niggle. If it has been gone over
thoroughly before, just point me to the related discussion thread. An SCL
interpretation I = (I,R,ext,V) uses a relation component R = (R_w, R_1, R_2,
...) that is a little strange -- it seems to serve only as a middleman
between relations symbols of an associated lexicon L and subsets of tuples
of the set of individuals I: relational denotation and extension is a pair
of composable functions
    V o ext : PredCon --> R --> Pow(I^w).
Can R be eliminated and a single extension/denotation function be used here.
This would seem to be a much simpler and more aesthetically pleasing
approach. I believe that this is related to endnote 5: "It is possible to
model of the members of R extensionally as sets, though this will in general
require non-well-founded set theory, since a relation, qua individual, can
be in its own extension." Is this true? Is the purpose of R to proscribe
self-membership? If so, how exactly does this work? Can we not just simplify
as mentioned above and verbally proscribe self-membership?

Robert E. Kent
rekent at ontologos.org