[SCL] slightly free logic

[pat hayes]

Chris, I'd be grateful if you could take a look at the current 
document Im trying to write  and particularly at 
http://www.ihmc.us/users/phayes/SCL-december.html#entailment

The issue is this. This now covers the full CL wild west syntax, and 
the model theory is unconventional but I think OK, except that 
quantification over functions could be empty. I am willing to live 
with this, myself, but it does have a kind of a smell of free logics 
about it that I know you have strong feelings about.

We could always retreat to the no-function-variables position, or the 
other alternative would be to insist that every interpretation has at 
least one function of every arity,  but that seems totally ad-hoc. I 
would be willing to put up with this slight oddity if we can retain 
the generality of the syntax. .
THis isnt written up yet, but theres a general way to translate any 
ontology into one without a header, by restricting the quantifiers 
suitably. THis adds a lot of extra stuff to the universe, of course, 
but it also makes all the quantifiers 'normal' since they range over 
named sets, and so if there are no 'functions' (they are individuals 
in the translation) then the empty quantifiers just have the form 
(forall (?x)(false ?x) implies ...) which of course makes perfect 
sense.

Anyway, gotta go to bed. Hopefully will get some more done tomorrow.

Pat


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