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␈↓ α∧␈↓␈↓ u1


␈↓ α∧␈↓α␈↓ ∧uTHE FRAME PROBLEM IN THE 1980s

␈↓ α∧␈↓␈↓ αTThe␈αMcCarthy-Hayes␈αframe␈α
problem␈αis␈αthat␈αof␈α
expressing␈αin␈αsome␈αformal␈α
system␈αcommon
␈↓ α∧␈↓sense␈α∪knowledge␈α∪of␈α∪what␈α∪remains␈α∪constant␈α∩when␈α∪changes␈α∪occur.␈α∪ This␈α∪information␈α∪must␈α∩be
␈↓ α∧␈↓expressed␈α∂in␈α∞a␈α∂feasible␈α∂and␈α∞plausible␈α∂way.␈α∞ In␈α∂particular,␈α∂it␈α∞is␈α∂neither␈α∞feasible␈α∂nor␈α∂plausible␈α∞to
␈↓ α∧␈↓suppose␈αthat␈α
every␈αexpression␈αof␈α
the␈αconsequences␈αof␈α
an␈αevent␈αlists␈α
everything␈αthat␈αdoesn't␈α
change
␈↓ α∧␈↓when␈α⊗the␈α↔event␈α⊗occurs.␈α↔ We␈α⊗will␈α↔discuss␈α⊗the␈α↔somewhat␈α⊗more␈α↔general␈α⊗problem␈α↔of␈α⊗giving
␈↓ α∧␈↓epistemologically adequate expressions of knowledge of the consequences of actions.

␈↓ α∧␈↓␈↓ αTSuppose␈α
a␈αgoal␈α
is␈α
to␈αbe␈α
achieved␈αby␈α
a␈α
sequence␈αof␈α
actions.␈α Each␈α
action␈α
has␈αpreconditions
␈↓ α∧␈↓for␈α
achieving␈α
its␈αintended␈α
effect,␈α
and␈αwe␈α
need␈α
assurance␈αthat␈α
each␈α
action␈αresults␈α
in␈α
a␈αsituation␈α
that
␈↓ α∧␈↓satisfies the preconditions for the next.

␈↓ α∧␈↓␈↓ αTOne␈αaspect␈αof␈αthis␈αis␈αthe␈αsimple␈αframe␈αproblem.␈α If␈αa␈αplan␈αis␈αto␈αmove␈αblock␈α␈↓↓A␈↓␈αonto␈αblock␈α␈↓↓B␈↓
␈↓ α∧␈↓and␈α
then␈αmove␈α
block␈α
␈↓↓C␈↓␈αonto␈α
block␈α
␈↓↓D,␈↓␈αwe␈α
must␈αbe␈α
assured␈α
that␈αmoving␈α
block␈α
␈↓↓A␈↓␈αdoesn't␈α
move␈α␈↓↓C␈↓␈α
to
␈↓ α∧␈↓a␈α∞place␈α∞from␈α∞which␈α∂it␈α∞can't␈α∞be␈α∞moved␈α∂and␈α∞that␈α∞moving␈α∞␈↓↓C␈α∂doesn't␈↓␈α∞destroy␈α∞the␈α∞effect␈α∂of␈α∞having
␈↓ α∧␈↓moved ␈↓↓A␈↓ first.

␈↓ α∧␈↓␈↓ αTIn␈αdescribing␈αaction␈αrules,␈αwe␈αprefer␈αa␈αlevel␈αof␈αdetail␈αat␈αwhich␈αactions␈αhave␈αdefinite␈αeffects.
␈↓ α∧␈↓In␈α
general,␈αgoals␈α
are␈α
given␈αat␈α
a␈αlesser␈α
level␈α
of␈αdetail␈α
than␈αis␈α
required␈α
for␈αdetermining␈α
the␈αeffects␈α
of
␈↓ α∧␈↓actions.␈α
 Therefore,␈α
we␈α
need␈α
to␈α
distinguish␈α
between␈α"states␈α
of␈α
affairs",␈α
which␈α
are␈α
at␈α
that␈α
level␈αof
␈↓ α∧␈↓detail, and propositional fluents which may be at a lesser level of detail.

␈↓ α∧␈↓␈↓ αTMore␈αgenerally␈αyet,␈αour␈αknowledge␈αof␈αthe␈αeffects␈αof␈αactions␈αmay␈αbe␈αat␈αa␈αlower␈αlevel␈αof␈αdetail
␈↓ α∧␈↓than␈α∞is␈α
required␈α∞to␈α
determine␈α∞the␈α
preconditions␈α∞for␈α
the␈α∞desired␈α
subsequent␈α∞actions.␈α∞ This␈α
forces
␈↓ α∧␈↓plans␈α∞to␈α∂contain␈α∞servos,␈α∂i.e.␈α∞␈↓αwhile␈↓␈α∂loops,␈α∞and␈α∞conditional␈α∂branches.␈α∞ Example:␈α∂if␈α∞we␈α∂have␈α∞many
␈↓ α∧␈↓heavy␈α
boxes␈αto␈α
move,␈α
our␈αplan␈α
envisages␈αresting␈α
whenever␈α
the␈αmoves␈α
have␈α
made␈αus␈α
tired,␈αbut␈α
our
␈↓ α∧␈↓knowledge␈α
of␈α
the␈α
effects␈α
of␈αmoving␈α
boxes␈α
is␈α
insufficient␈α
to␈αdetermine␈α
when␈α
we␈α
will␈α
be␈αtired.␈α
 Thus
␈↓ α∧␈↓using incomplete states of affairs is mitigated by including servos in the plans.

␈↓ α∧␈↓␈↓ αTNotes for and about meeting jan 28.

␈↓ α∧␈↓1.␈αWhy␈αshould␈αphilosophers␈αbe␈αinterested␈αin␈αthe␈αframe␈αproblem.␈α Dan␈αsays␈αyes,␈αand␈αJohn␈αH.␈αstill
␈↓ α∧␈↓has questions.

␈↓ α∧␈↓2.␈α
The␈αframe␈α
problem␈αmay␈α
be␈αthe␈α
left␈αear␈α
of␈αthe␈α
elephant.␈α The␈α
elephant␈αmay␈α
be␈αthe␈α
qualification
␈↓ α∧␈↓problem.␈α Pat␈αHayes␈αthinks␈αthe␈αframe␈αproblem␈αis␈αseparate␈αand␈αeasier,␈αbut␈αthis␈αis␈αperhaps␈αbecause
␈↓ α∧␈↓he␈α∞thinks␈α
histories␈α∞solve␈α∞the␈α
problem.␈α∞ He␈α∞had␈α
some␈α∞worthwhile␈α∞ways␈α
of␈α∞expressing␈α∞things,␈α
but
␈↓ α∧␈↓they all seemed translatable to the situation formalism.

␈↓ α∧␈↓3. The frame axioms discussed were

␈↓ α∧␈↓␈↓ αT␈↓↓∀xyzws.[z ≠ x ⊃ [on(z,w,result(move(x,y),s)) ≡ on(z,w,s)]]␈↓

␈↓ α∧␈↓␈↓ αT␈↓↓∀u x y s.[color(u,result(move(x,y),s)) = color(u,s)]␈↓

␈↓ α∧␈↓and the state vector form

␈↓ α∧␈↓␈↓ αT␈↓↓∀var1␈α∩var2␈α∩val␈α∩state.[value(var2,assign(var1,val,state))␈α∩=␈α⊃␈↓αif␈↓↓␈α∩var1␈α∩=␈α∩var2␈α∩␈↓αthen␈↓↓␈α∩val␈α⊃␈↓αelse␈↓↓
␈↓ α∧␈↓↓value(var2,state)]␈↓.
␈↓ α∧␈↓␈↓ u2


␈↓ α∧␈↓This needs to be decorated with a better explanation of its relation to frames as objects.

␈↓ α∧␈↓4. STRIPS - nothing changes except what is said to change.

␈↓ α∧␈↓vs.

␈↓ α∧␈↓circumscription - nothing changes except what can bbe shown to change.

␈↓ α∧␈↓5.␈α∩Models␈α∩vs.␈α⊃common␈α∩sense␈α∩information.␈α⊃ Models␈α∩have␈α∩to␈α⊃be␈α∩surrounded␈α∩by␈α∩common␈α⊃sense
␈↓ α∧␈↓information␈α
so␈α
that␈α
the␈α
robot␈α
will␈α
not␈α
be␈α
dumfounded␈α
when␈α
some␈α
of␈α
the␈αcircumscriptions␈α
involved
␈↓ α∧␈↓in their creation have to be retracted.

␈↓ α∧␈↓6.␈α
The␈α∞fact␈α
that␈α
what␈α∞we␈α
know␈α
about␈α∞the␈α
effects␈α
of␈α∞an␈α
action␈α
is␈α∞often␈α
insufficient␈α
to␈α∞assure␈α
the
␈↓ α∧␈↓prerequisites␈αof␈αthe␈αnext␈αaction␈αis␈αmitigated␈αby␈αthe␈αuse␈αof␈αservomechanisms.␈α The␈αlogical␈αservo␈αof
␈↓ α∧␈↓the Huberman chess program was mentioned.

␈↓ α∧␈↓7. Variable detail indices were expounded but not well enough to get much response.

␈↓ α∧␈↓8. Peter Cheeseman (from Australia?) and Lew Creary took part.

␈↓ α∧␈↓9.␈α
The␈α
relation␈α
to␈α∞philosophy␈α
question␈α
was␈α
interrupted␈α
many␈α∞times,␈α
but␈α
eventually␈α
began␈α∞to␈α
fly.
␈↓ α∧␈↓Continuation Friday at 2:30.

␈↓ α∧␈↓Mathematical models

␈↓ α∧␈↓␈↓ αTIn␈α∞science,␈α∞it␈α∞is␈α∞customary␈α∞to␈α∞use␈α∞"mathematical␈α∞models"␈α∞of␈α∞the␈α∞phenomena␈α∞being␈α
studied.
␈↓ α∧␈↓Our␈α∂view␈α∂is␈α∂that␈α∂common␈α∂sense␈α∂knowledge␈α∞of␈α∂a␈α∂phenomenon␈α∂cannot␈α∂usually␈α∂be␈α∂formulated␈α∞in
␈↓ α∧␈↓terms␈α
of␈α
a␈αmathematical␈α
model␈α
of␈α
the␈αkind␈α
used,␈α
because␈α
the␈αcommon␈α
sense␈α
knowledge␈α
does␈αnot
␈↓ α∧␈↓provide␈α∂enough␈α∞information.␈α∂ Finding␈α∞a␈α∂mathematical␈α∞model␈α∂is␈α∞an␈α∂intellectual␈α∂achievement␈α∞not
␈↓ α∧␈↓always␈α∃possible.␈α∃ When␈α∃it␈α∀is␈α∃possible,␈α∃it␈α∃requires␈α∀disregarding␈α∃some␈α∃of␈α∃the␈α∃common␈α∀sense
␈↓ α∧␈↓information,␈αso␈α
that␈αdeciding␈α
when␈αand␈α
how␈αto␈α
apply␈αthe␈α
model␈αrequires␈α
the␈αuse␈α
of␈αcommon␈α
sense
␈↓ α∧␈↓information that we have not succeeded in including in the model.

␈↓ α∧␈↓␈↓ αTWe␈αshall␈α
elaborate␈αthis␈α
point.␈α Consider␈αa␈α
mathematical␈αmodel␈α
of␈αa␈α
dynamic␈αphenomenon.
␈↓ α∧␈↓Specifying␈α
the␈αmodel␈α
requires␈αdefining␈α
a␈αstate␈α
space␈αand␈α
giving␈αits␈α
laws␈αof␈α
motion.␈α Specifying␈α
the
␈↓ α∧␈↓state␈αspace␈αrequires␈αconfining␈αour␈αattention␈αto␈αto␈αcertain␈αaspects␈αof␈αthe␈αworld.␈α If␈αother␈αaspects␈αof
␈↓ α∧␈↓the␈αworld␈αcan␈αaffect␈αhow␈α
the␈αaspects␈αof␈αour␈αconcern␈αchange,␈α
this␈αcan␈αonly␈αbe␈αknown␈α
by␈αcommon
␈↓ α∧␈↓sense␈α
reasoning␈α
outside␈αthe␈α
model.␈α
 To␈α
take␈αan␈α
extreme␈α
example,␈αour␈α
model␈α
of␈α
the␈αgravitational
␈↓ α∧␈↓interactions␈α
of␈α
the␈α
solar␈αsystem␈α
allows␈α
predictions␈α
for␈α
hundreds␈αof␈α
thousands␈α
of␈α
years␈α
and␈αcould
␈↓ α∧␈↓be␈α
embodied␈α
in␈αa␈α
computer␈α
program␈α
that␈αwould␈α
give␈α
the␈α
jposition␈αof␈α
aplanet␈α
over␈α
such␈αperiods␈α
of
␈↓ α∧␈↓time.␈α∂ However,␈α∂everyone␈α∞knows␈α∂that␈α∂a␈α∞hitherto␈α∂unobserved␈α∂planet␈α∞sized␈α∂body␈α∂might␈α∂enter␈α∞the
␈↓ α∧␈↓solar␈αsystem␈αfrom␈αthe␈αoutside␈αand␈αobviate␈αthe␈αcomputations,␈αand␈αthe␈αmodel␈αalso␈αdoesn't␈αtake␈αinto
␈↓ α∧␈↓account␈αthe␈αpossibility␈αthat␈αhumanity␈αmight␈αacquire␈αthe␈αability␈αand␈αmotivation␈αto␈αalter␈αthe␈αcourse
␈↓ α∧␈↓of␈α
the␈α
planets␈α
The␈α
information␈α
we␈α∞possess␈α
about␈α
what␈α
humanity␈α
might␈α
do␈α
cannot␈α∞be␈α
integrated
␈↓ α∧␈↓into the model, certainly not just by considering the Newtonian and Einsteinian laws of gravity.

␈↓ α∧␈↓␈↓ αTWhen␈αwe␈αcome␈αto␈αbiological␈αphenomena,␈αthe␈αsituation␈αis␈αworse.␈α Since␈αthe␈α1920s␈αthere␈αhave
␈↓ α∧␈↓been␈α⊗elegant␈α⊗predator-prey␈α∃differential␈α⊗equation␈α⊗models,␈α⊗but␈α∃they␈α⊗don't␈α⊗take␈α⊗into␈α∃account
␈↓ α∧␈↓emigration␈α∩from␈α∪good␈α∩areas␈α∪for␈α∩a␈α∪species␈α∩to␈α∪areas␈α∩whose␈α∪population␈α∩depends␈α∪on␈α∩occasional
␈↓ α∧␈↓immigration.
␈↓ α∧␈↓␈↓ u3


␈↓ α∧␈↓␈↓ αTWhen␈α
we␈α
come␈αto␈α
common␈α
sense␈αphysics,␈α
the␈α
situation␈αis␈α
yet␈α
worse.␈α The␈α
basic␈α
problem␈αis
␈↓ α∧␈↓that␈α
what␈α
we␈α
know␈αabout␈α
the␈α
consequences␈α
of␈αan␈α
event␈α
is␈α
usually␈αinsufficient␈α
to␈α
say␈α
what␈αevent
␈↓ α∧␈↓will␈α
occur␈α
next.␈α∞ Our␈α
knowledge␈α
of␈α∞the␈α
possibilities␈α
does␈α∞not␈α
take␈α
the␈α∞form␈α
of␈α
an␈α∞assignment␈α
of
␈↓ α∧␈↓probabilities␈α∞to␈α∞events␈α∞in␈α∞a␈α∞definite␈α∞sample␈α∞space.␈α∞ The␈α∞formation␈α∞of␈α∞a␈α∞probabilistic␈α∞model␈α∞also
␈↓ α∧␈↓requires␈α∀simplifying␈α∀assumptions␈α∀that␈α∀force␈α∀the␈α∀model␈α∀to␈α∀be␈α∀surrounded␈α∀by␈α∀common␈α∀sense
␈↓ α∧␈↓information.

␈↓ α∧␈↓␈↓ αTThe␈αeffects␈αof␈αan␈αaction␈αor␈αevent␈αare␈αtypically␈αdescribed␈αin␈αEnglish␈αby␈αsaying␈α
what␈αaspects
␈↓ α∧␈↓of␈αthe␈αworld␈αthe␈αevent␈α(we␈αshall␈αinclude␈αactions␈αunder␈αevents)␈αchanges,␈αand␈αhow␈αit␈αchanges␈αthem.
␈↓ α∧␈↓If␈α∂we␈α∂want␈α⊂a␈α∂sufficient␈α∂description␈α⊂of␈α∂the␈α∂situation␈α∂that␈α⊂results␈α∂from␈α∂an␈α⊂event␈α∂so␈α∂that␈α⊂we␈α∂can
␈↓ α∧␈↓determine␈α∞the␈α∞effects␈α∞of␈α∞future␈α∞actions,␈α∞we␈α∞need␈α∞to␈α∞know␈α∞what␈α∞doesn't␈α∞change,␈α∞and␈α∞this␈α∂is␈α∞most
␈↓ α∧␈↓things.␈α∃ However,␈α∃this␈α∃is␈α∃usually␈α∃not␈α∃described␈α∃in␈α∃English␈α∃(it␈α∃is␈α∃somehow␈α∃implicit␈α∃in␈α∀the
␈↓ α∧␈↓conversational␈α≠situation),␈α≠so␈α≠that␈α≠formalizing␈α≠it␈α≠requires␈α≠identifying␈α≠the␈α≠common␈α≠sense
␈↓ α∧␈↓presumptions␈α
about␈α
what␈α
doesn't␈αchange.␈α
 This␈α
is␈α
called␈αthe␈α
frame␈α
problem,␈α
because␈αin␈α
(McCarthy
␈↓ α∧␈↓and␈α⊃Hayes␈α⊃1970),␈α⊃it␈α⊃was␈α⊃supposed␈α⊃that␈α⊃the␈α⊃independent␈α⊃aspects␈α⊃of␈α⊃the␈α⊃world␈α⊃were␈α⊃might␈α⊂be
␈↓ α∧␈↓regarded␈αas␈αattached␈αto␈αa␈α"frame␈αof␈αreference"␈αlike␈αthe␈αco-ordinate␈αsystems␈αused␈αin␈αphysics.␈α One
␈↓ α∧␈↓rather␈α∀naive␈α∀"solution"␈α∀to␈α∀the␈α∀frame␈α∀problem␈α∀is␈α∀to␈α∀postulate␈α∀that␈α∀everything␈α∀not␈α∪explicitly
␈↓ α∧␈↓described␈α
as␈α
changing␈α∞remains␈α
unchanged.␈α
 This␈α
idea␈α∞is␈α
embodied␈α
in␈α
SRI's␈α∞STRIPS␈α
formalism.
␈↓ α∧␈↓Its␈α∞use␈α∞requires␈α∂that␈α∞language␈α∞be␈α∞used␈α∂in␈α∞restricted␈α∞way,␈α∞and␈α∂the␈α∞STRIPS␈α∞programs␈α∂obey␈α∞such
␈↓ α∧␈↓restrictions.␈α
 For␈α
example,␈α
if␈α
we␈α
describe␈α
blocks␈αon␈α
a␈α
table␈α
using␈α
the␈α
predicate␈α
on(x,y)␈αspecifying
␈↓ α∧␈↓that␈α⊂block␈α⊂x␈α⊂is␈α∂on␈α⊂block␈α⊂y␈α⊂in␈α∂a␈α⊂situation␈α⊂implicitly␈α⊂specified,␈α∂then␈α⊂we␈α⊂can␈α⊂describe␈α⊂actions␈α∂as
␈↓ α∧␈↓effecting␈αthe␈αtruth␈αor␈αfalsity␈αof␈α
various␈αon(x,y)␈αstatements.␈α However,␈αthis␈αconvention␈α
prevents␈αus
␈↓ α∧␈↓from␈α∩introducing␈α∩a␈α∩derived␈α∩predicate␈α∩above(x,y),␈α∩since␈α∩above(x,y)␈α∩statements␈α∩are␈α∩changed␈α∩by
␈↓ α∧␈↓changing␈α⊂on(x,y)␈α∂statements.␈α⊂ This␈α∂can␈α⊂be␈α∂repaired␈α⊂by␈α∂regarding␈α⊂certain␈α∂of␈α⊂the␈α⊂predicates␈α∂like
␈↓ α∧␈↓on(x,y)␈α∂as␈α∂primary␈α∂and␈α⊂others␈α∂like␈α∂above(x,y)␈α∂as␈α∂secondary.␈α⊂ However,␈α∂when␈α∂we␈α∂look␈α⊂at␈α∂larger
␈↓ α∧␈↓domains␈α⊂of␈α⊂common␈α⊂sense␈α∂knowledge,␈α⊂it␈α⊂doesn't␈α⊂seem␈α∂that␈α⊂we␈α⊂have␈α⊂a␈α∂clear␈α⊂notion␈α⊂of␈α⊂what␈α∂is
␈↓ α∧␈↓primary␈α
and␈α∞what␈α
is␈α∞secondary.␈α
 For␈α∞example,␈α
suppose␈α
we␈α∞say␈α
that␈α∞Pat␈α
went␈α∞from␈α
Palo␈α∞Alto␈α
to
␈↓ α∧␈↓Boston.␈α Did␈α
his␈αwife␈α
or␈αcar␈α
or␈αclothes␈α
go␈αwith␈α
him?␈α The␈α
answer␈αdepends␈α
on␈αwhether␈αthe␈α
"going"
␈↓ α∧␈↓is to be interpreted as a permanent move or just a trip.

␈↓ α∧␈↓␈↓ αT␈↓↓on(x,y)␈↓␈α∂is␈α∞a␈α∂quasi-proposition.␈α∂ It␈α∞can␈α∂only␈α∂have␈α∞a␈α∂truth␈α∞value␈α∂in␈α∂a␈α∞context.␈α∂ There␈α∂is␈α∞a
␈↓ α∧␈↓predicate␈α⊃␈↓↓holds␈↓␈α⊂so␈α⊃that␈α⊂␈↓↓holds(on(x,y),qt)␈↓␈α⊃is␈α⊃the␈α⊂assertion␈α⊃that␈α⊂␈↓↓on(x,y)␈↓␈α⊃holds␈α⊂in␈α⊃the␈α⊃context␈α⊂qt.
␈↓ α∧␈↓Quasi-propositions␈α
are␈αcombined␈α
by␈α
quasi-boolean␈αoperators␈α
␈↓↓and,␈↓␈α␈↓↓or␈↓␈α
and␈α
␈↓↓not.␈↓␈αWe␈α
do␈αnot␈α
require
␈↓ α∧␈↓that␈α
one␈α
of␈α
␈↓↓holds(p,qt)␈↓␈α
or␈α␈↓↓holds(not p,qt)␈↓␈α
be␈α
true,␈α
because␈α
the␈αcontext␈α
qt␈α
may␈α
not␈α
be␈αsufficiently
␈↓ α∧␈↓detailed to determine a truth value for ␈↓↓p. We␈↓ will have

␈↓ α∧␈↓␈↓ αT␈↓↓holds(p and q,qt) ≡ holds(p,qt) ∧ holds(q,qt)␈↓

␈↓ α∧␈↓␈↓ αTand

␈↓ α∧␈↓␈↓ αT␈↓↓¬(holds(p,qt) ∧ holds(not p,qt))␈↓.

␈↓ α∧␈↓␈↓ αTWe may or may not postulate

␈↓ α∧␈↓␈↓ αT␈↓↓holds(p or q,qt) ≡ holds(p,qt) ∨ holds(q,qt)␈↓.

␈↓ α∧␈↓␈↓ αTContexts␈α∞may␈α∂be␈α∞ordered,␈α∞whereby␈α∂qt␈α∞≤␈α∞qt'␈α∂means␈α∞that␈α∞context␈α∂qt'␈α∞has␈α∂more␈α∞information
␈↓ α∧␈↓than context qt, leading to

␈↓ α∧␈↓␈↓ αT␈↓↓qt ≤ qt' ∧ holds(p,qt) ⊃ holds(p,qt').
␈↓ α∧␈↓␈↓ u4


␈↓ α∧␈↓␈↓ αTThe␈α
idea␈α
is␈α
that␈α
however␈α
detailed␈α
a␈α
context␈α
may␈α
be,␈α
there␈α
will␈α
be␈α∞quasi-propositions␈α
that
␈↓ α∧␈↓require␈α∀yet␈α∪more␈α∀details␈α∪to␈α∀decide.␈α∪ There␈α∀might␈α∪be␈α∀a␈α∪similar␈α∀dual␈α∪relation␈α∀among␈α∪quasi-
␈↓ α∧␈↓propositions, satisfying

␈↓ α∧␈↓␈↓ αT␈↓↓p ≤ p' ∧ holds(p',qt) ⊃ holds(p,qt)␈↓.  The Frame Problem as a Philosophical Problem

␈↓ α∧␈↓␈↓ αTIt␈α⊃is␈α⊃not␈α⊃obvious␈α⊃that␈α⊃the␈α∩frame␈α⊃problem␈α⊃fits␈α⊃into␈α⊃the␈α⊃previously␈α⊃recognized␈α∩classes␈α⊃of
␈↓ α∧␈↓problems.

␈↓ α∧␈↓␈↓ αTConsider␈α⊗the␈α↔consequences␈α⊗of␈α↔spilling␈α⊗a␈α↔cup␈α⊗of␈α↔coffee.␈α⊗ Let␈α↔us␈α⊗suppose␈α↔that␈α⊗these
␈↓ α∧␈↓consequences␈α~are␈α~covered␈α~sufficiently␈α~accurately␈α~by␈α~the␈α~known␈α~laws␈α~of␈α≠mechanics␈α~and
␈↓ α∧␈↓hydrodynamics.␈α∞ Suppose␈α
this␈α∞has␈α
been␈α∞verified␈α
by␈α∞experiments␈α
using␈α∞accurately␈α∞measured␈α
cups
␈↓ α∧␈↓with␈α⊃accurately␈α⊃measured␈α⊃amounts␈α⊃of␈α⊃copy␈α⊃whose␈α⊃viscosity,␈α⊃density,␈α⊃etc.␈α⊃have␈α∩been␈α⊃accurately
␈↓ α∧␈↓measured,␈α⊃and␈α⊃we␈α⊂are␈α⊃interested␈α⊃in␈α⊃its␈α⊂being␈α⊃spilled␈α⊃on␈α⊂surfaces␈α⊃whose␈α⊃properties␈α⊃have␈α⊂been
␈↓ α∧␈↓measured.␈α∩ Anyway␈α∩assume␈α∩that␈α∩the␈α∩results␈α∩of␈α∩experiments␈α∩correspond␈α∩to␈α∩thsse␈α∩predicted␈α∩by
␈↓ α∧␈↓theory.

␈↓ α∧␈↓␈↓ αTNext␈αsuppose␈α
a␈αcup␈α
of␈αcoffee␈α
is␈αto␈α
be␈αspilled␈α
under␈αconditions␈α
that␈αpermit␈αno␈α
measurements,
␈↓ α∧␈↓and␈α⊃people␈α⊃react␈α⊃to␈α⊃the␈α⊃event.␈α⊃ Also␈α⊃consider␈α⊃a␈α⊃report␈α⊃of␈α⊃such␈α⊃an␈α⊃event.␈α⊃ Indeed␈α⊃consider␈α⊂a
␈↓ α∧␈↓hypothetical␈α⊃wire␈α⊃service␈α⊃news␈α⊃story␈α⊃beginning␈α⊃␈↓↓"Coffee␈α⊃spill␈α⊃kills␈α⊃three.␈α⊃ Three␈α⊃fellows␈α⊃of␈α⊃the
␈↓ α∧␈↓↓Center␈α∞for␈α∞Advanced␈α∞Study␈α∞in␈α∞Behavioral␈α∞Sciences␈α∞in␈α∞Stanford,␈α∞California␈α∞were␈α∞scalded␈α∂to␈α∞death
␈↓ α∧␈↓↓when␈αone␈αof␈αthem␈αinadvertently␈αknocked␈αover␈αa␈αcup␈αof␈αcoffee"␈↓.␈α Common␈αsense␈αphysics␈αtells␈αus␈αthat
␈↓ α∧␈↓this not possible.

␈↓ α∧␈↓␈↓ αTThe␈αfacts␈αthat␈αwe␈αuse␈αare␈αnot␈αpart␈αof␈αpsychology,␈αbecause␈αthey␈αdeal␈αwith␈αthe␈αphysical␈αworld
␈↓ α∧␈↓and␈α
would␈α
be␈α
the␈α
same␈α
if␈α
the␈α
reasoner␈α
were␈α
a␈α
robot.␈α
 They␈α
are␈α
not␈α
part␈α
of␈α
physics␈α
as␈α
presently
␈↓ α∧␈↓conceived␈α∂which␈α∂is␈α∂entirely␈α∂satisfied␈α∂if␈α⊂the␈α∂laws␈α∂of␈α∂hydrodynamics␈α∂are␈α∂adequate␈α∂to␈α⊂predict␈α∂the
␈↓ α∧␈↓phenomenon␈α∃given␈α∃accurate␈α∃measurements.␈α∃ Some␈α⊗may␈α∃regard␈α∃them␈α∃as␈α∃too␈α⊗specialized␈α∃for
␈↓ α∧␈↓philosophy.␈α
 What␈α
is␈α
probably␈α
not␈α
too␈α
specialized␈α
is␈α
the␈α
study␈α
of␈α
how␈α
it␈α
is␈α
possible␈α∞to␈α
represent
␈↓ α∧␈↓the knowledge that permits common sense answers to the questions?

␈↓ α∧␈↓␈↓ αTQueries:

␈↓ α∧␈↓␈↓ αTIs␈α≠McCarthy's␈α≠distinction␈α≠between␈α≠collections␈α≠of␈α≠facts␈α≠and␈α≠models␈α≠obtained␈α~from
␈↓ α∧␈↓circumscribing␈αthese␈α
facts␈αneeded?␈α
 (Incidentally,␈αI␈αfear␈α
a␈αcollision␈α
between␈αthis␈α
use␈αof␈α"model"␈α
and
␈↓ α∧␈↓that␈αof␈α"model␈αtheory".␈α Up␈αto␈αnow␈αthese␈αtwo␈αsubjects␈αhave␈αbeen␈αtoo␈αfar␈αapart␈αfor␈αthe␈αconflict␈αto
␈↓ α∧␈↓matter, but this may not continue).

␈↓ α∧␈↓␈↓ αTDo we need indices capable of indefinite refinement?

␈↓ α∧␈↓␈↓ αTIs␈α∂the␈α∂frame␈α∞problem␈α∂best␈α∂treated␈α∞as␈α∂a␈α∂case␈α∞of␈α∂the␈α∂qualification␈α∞problem?␈α∂ A␈α∂good␈α∞static
␈↓ α∧␈↓qualification problem would help in comparing.