[SCL] revised draft and comments needed

[Pat Hayes]

Folks, in case anyone is still reading this stuff, there is a 
slightly updated draft now at

http://www.ihmc.us/users/phayes/SCL_current_2004.html

and I will be using this URL until further notice. This is still 
incomplete, but has numerous errors fixed and has a somewhat improved 
presentation of the model theory, so anyone who is actually USING the 
thing should use this version and destroy any older copies.

I would be grateful for any feedback (positive or negative) from 
other group members on the way that the basic language is shaping up, 
particularly the way that the semantics is presented.

Chris (and Tanel), this handles the full wild west syntax, no 
restrictions on where names occur, with I think minimal changes from 
a conventional GOFOL MT. The chief oddity arises from the 
function/relation convention, since

1: (= x (R y z))

entails

2:  (R x y z)

but not the reverse (as one would expect); but in spite of this asymmetry,

3.  (iff   (= x (R y z))  (R x y z) )

is a tautology, since the mere USE of R in a functional position in a 
text requires it to be interpreted as functional.  This means that 
for example 2 does not entail 1, but (2 + 1) does entail 1.

I think this is inevitable, given the combination of the WW syntax 
freedom and the requirement of being able to combine any two texts 
regardless of their form. It means however that the deduction theorem 
isnt generally true, things like that.

BTW, the way this issue appears in the holds/app translation is that 
one has to include axioms of the form

(= x (app y @z)) implies (holds y x @z))

in the target translation *just when y occurs in a function position* 
(not otherwise), and these are what screw up the entailments, since 
this will be included in the translation of (1 + 2 ) but not in that 
of 2 by itself.

Comments on the above? Can we live with this?

Pat



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