perm filename SCOTT.XGP[LET,JMC]1 blob sn#124975 filedate 1974-10-16 generic text, type T, neo UTF8
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STANFORD ARTIFICIAL INTELLIGENCE LABORATORY
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␈↓ ∧αDEPARTMENT OF COMPUTER SCIENCE
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␈↓ ¬	STANFORD UNIVERSITY
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␈↓ ∧;STANFORD, CALIFORNIA 94305
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␈↓ α_␈↓ αh␈↓ β8␈↓ ∧λ␈↓ ∧X␈↓ ¬(
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␈↓ α_␈↓ αh␈↓ β8␈↓ ∧λ␈↓ ∧X␈↓ ¬(␈↓ ¬x14 October 1974
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Professor Dana Scott
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Mathematical Institute
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24-29 St. Giles
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Oxford OX1 3LB
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England
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Dear Dana:
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␈↓ α_John␈αGill␈αgave␈αme␈αyour␈α␈↓↓Data␈αTypes␈αas␈αLattices␈↓␈αand␈αthank␈αyou␈αvery␈αmuch.␈α
I␈α
am␈α
still␈α
pursuing
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␈↓ ↓Hmy␈αidea␈αof␈αtrying␈αto␈αget␈αa␈αsystem␈αthat␈αwill␈αallow␈αthe␈αcontinuous␈αfunctions␈αto␈αbe␈αaxiomatized␈αin␈αfirst
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␈↓ ↓Horder␈αlogic␈αso␈αthat␈αwe␈αcan␈αcombine␈αreasoning␈αabout␈αother␈αentities␈αwith␈αreasoning␈αabout␈αcomputable
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␈↓ ↓Hfunctions.␈α
To␈α
this␈α
end,␈α
about␈α
two␈α
years␈αago,␈αI␈αintroduced␈αthe␈αidea␈αof␈αextensional␈αforms:␈αan␈αe.f.␈αhas
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␈↓ ↓Hfree␈αvariables␈αin␈αit,␈αbut␈αtwo␈αof␈αthem␈αare␈αequal␈αif␈αthey␈αgive␈αthe␈αsame␈αvalues␈αfor␈αall␈αvalues␈αof␈α
the␈α
free
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␈↓ ↓Hvariables.␈αThe␈αλ␈αbecomes␈αjust␈αanother␈αfunction␈αthat␈αcombines␈αa␈αvariable␈αand␈αa␈αform␈αto␈αget␈αanother
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␈↓ ↓Hform␈αhaving␈αone␈αless␈αvariable.␈α
The␈α
idea␈α
seems␈α
to␈α
work␈α
out,␈α
but␈α
I␈α
haven't␈α
pushed␈α
it␈α
quite␈α
far␈α
enough
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␈↓ ↓Hto␈α
really␈α
see.
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␈↓ α_Your␈α∞latest␈α∞seems␈α∞promising␈α∞from␈α∞my␈α∞point␈α∞of␈α∞view,␈α∞because␈α∞it␈α∞gets␈α
all␈α
entities␈α
down␈α
into␈α
a
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␈↓ ↓Hfixed␈α∞domain,␈α∞e.g.␈α∞Pw,␈α∞and␈α∞this␈α∞should␈α∞make␈α∞set-theoretic␈α
axiomatization␈α
easier.␈α
It␈α
occurred␈α
to␈α
me
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␈↓ ↓Hthat␈α∃for␈α∃practical␈α∃purposes␈α∃it␈α∃might␈α∃be␈α∀even␈α∀better␈α∀to␈α∀use␈α∀Ps,␈α∀where␈α∀s␈α∀is␈α∀the␈α∀set␈α∀of␈α∀LISP
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␈↓ ↓HS-expressions.␈α
Then␈α
the␈α
pairing␈α
functions,␈α
etc.␈α
that␈α
you␈α
use␈α
will␈α
be␈α
␈↓↓conveniently␈↓␈α
computable.
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␈↓ α_Enclosed␈α∞is␈α∞a␈α∞printout␈α∞of␈α∞a␈α∞set␈α∞of␈α∞axioms␈α∞for␈α∞extensional␈α
forms,␈α
but␈α
I␈α
am␈α
not␈α
sure␈α
they␈α
are
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␈↓ ↓Hcomprehensible␈α
without␈α
more␈α
talk.
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                                                ␈↓ ¬xBest Regards,
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␈↓ α_ ␈↓ αh␈↓ β8␈↓ ∧λ␈↓ ∧X␈↓ ¬(        John McCarthy
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␈↓ α_␈↓ αh␈↓ β8␈↓ ∧λ␈↓ ∧X␈↓ ¬(␈↓ ¬xDirector, Artificial Intelligence Laboratory
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␈↓ α_␈↓ αh␈↓ β8␈↓ ∧λ␈↓ ∧X␈↓ ¬(␈↓ ¬xProfessor of Computer Science
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JMC;paw
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scott.le1[let,jmc]:SU-AI
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