[SCL] Re: Observation

[Chris Menzel]

I just realized I may have clarified your point instead of mine.  To
avoid adding a new relation for "Holds" rather gratuitously to R, I just
clobbered R altogether and assigned extensions to predicates directly.
But that also clobbered the trivial point I was wanting to make.  So let
me revise the picture just a bit to make that point, and celebrate its
triviality:

SCL LEXICON

Predicates: P, Q, Rel
Indcons: P, a

INTERPRETATION

I = {1,2,3,4,5}
R = {5,10,15}

ext(5)  = {1,3,5)
ext(10) = {<1,2>, <4,5>)
ext(15) = {5}

V("P") = 5
V("Q") = 10
V("Rel") = 15
V("a") = 1

Note the interpretation of "Rel" is I intersect R = {5}, 5 being the
lone "reified" property or relation in this interpretation.  All I had
in mind as the GOFOL counterpart was an App/Holds transmogrification of
the language, in which predicate-only SCL predicates would remain
predicates and receive the extensions of their denotations as semantic
values, whereas SCL predicates designating individuals become GOFOL
indcons.  Thus:

TRANSMOG_LEXICON

Preds:  Q, Rel, Holds
Indcons: P, a

TRANSMOG_INTEPRETATION

I as above.
R* = {5,10,15,20}

ext(5)  = {1,3,5)
ext(10) = {<1,2>, <4,5>)
ext(15) = {5} (= R intersect I)
ext(20) = {<5,1>, <5,3>, <5,5>}

V*("P") = 5
V*("Q") = 10
V*("Rel") = 15 
V*("Holds") = 20
V*("a") = 1

So now the set of relations is still nonempty, as in the SCL
interpretation, but with an extra element.

That's all I meant.

-chris