[SCL] proposition variables in SCL??

[Pat Hayes]

Feedback welcomed on the following issue.

-------

Mark Stickel made the following comment:

>
>================
>
>It is perhaps worth noting in the text that
>  (implies P Q)
>is not legal SCL; it must be written as
>  (implies (P) (Q))
>I did not notice this at first; it hit me
>when you wrote that all sentences include parentheses.

Which made me think of the possibility of allowing proposition names 
into SCL. Right now we don't have names denoting propositions, only 
relations and individuals.

Do you think there is a use case for allowing propositional names in 
SCL?  Does anyone (know people who) actually need to be able to write 
(implies P Q) ?

Here's the rub. Following the, er, logic of the current introduction, 
if we have proposition names then they ought to survive punning with 
other names, in particular with individuals: so it ought to be 
possible to quantify over them, which is definitely not standard FO 
syntax; not even standard HO syntax, in fact.

However, with our semantics, they could be, and in fact it would be 
rather elegant, since then they would denote entities with 
truth-functional extensions, i.e. genuine propositions.

Here's how it would go: a name P can now have *three* kinds of 
extension: a truth-value, a relation(al extension) and a function; 
and they all can be 'folded' onto the denotation of the name. You CAN 
write things like
(iff P (P))
but you aren't obliged to specify any connection. And you can (that 
is, it makes semantic sense to) write things like
(exists (P)  P)
which could even be false in some interpretations. As far as I can 
see, this introduces no new tautologies.

In sum: this would be easy to do and might make SCL more powerful and 
expressive for some users, but it makes the language less 
conventional in ways that might give some people the horrors.

Any comments?

Pat



-- 
---------------------------------------------------------------------
IHMC	(850)434 8903 or (650)494 3973   home
40 South Alcaniz St.	(850)202 4416   office
Pensacola			(850)202 4440   fax
FL 32501			(850)291 0667    cell
phayes at ihmc.us       http://www.ihmc.us/users/phayes