hidden FO MT claim (was: [SCL] 'moderately' folded semantics)

[Robert E. Kent]

> This does not extend the universe. The 'harm' is done (i.e. 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.

On second thought, do you not think that there is a "hidden claim" in the FO
MT that there exists a class of individuals -- denote this by ' I '. Then
the SCL text corresponding to the above FOL text might be either

(forall (x I(x)) (= x a))
(P a)
(not (Q a))

or the more complete SCL text

(forall (x I(x)) (= x a))
(P a)
(not (Q a))
(not (I P))
(not (I Q))
(not (I I))

The relation ' I ' is being used to define the range of FO quantification,
and in the translation would "guard" all quantifications.

Robert E. Kent
rekent at ontologos.org