[SCL] 'moderately' folded semantics

[Robert E. Kent]

> This does not extend the universe. The 'harm' is done (ie the MT
> fails to correspond to a conventional FO MT) in the case where a
> relation name used purely relationally forces the universe to contain
> entities that it would not otherwise contain, as in Horrock's example:
>
> (forall (x) (= x a))
> (P a)
> (not (Q a))
>
> which is FO satisfiable, and SCL satisfiable (with an identical
> model) but does not have a satisfying moderately folded
> interpretation.

OK, I understand. This also answers a question that I had about the
distinction between an name such as 'P' and a composite term with empty
sequence such as '(P)'. For example, the above model would not satisfy the
text
(forall (x) (= x a))
((P) a)
(not ((Q) a))

However, I believe that I can still define an abstract or some-what
test-independent vocabulary. I will want all composite terms to be in object
position. But I need to allow the possibility that some names are in
relation or function position that are not in object position. Does this
sound OK to you?

Robert E. Kent
rekent at ontologos.org