/LMAR=0/XLINE=3/FONT#0=BAXL30/FONT#1=BAXM30/FONT#2=BASB30/FONT#3=SUB/FONT#4=SUP/FONT#5=BASL35/FONT#6=NGR25/FONT#7=MATH30/FONT#8=FIX25/FONT#9=GRKB30/FONT#12=CLAR30
␈↓ α∧␈↓␈↓ u1


␈↓ α∧␈↓␈↓ ∧8EPISTEMOLOGICAL PROBLEMS
␈↓ α∧␈↓␈↓ εgOF
␈↓ α∧␈↓␈↓ ∧\ARTIFICIAL INTELLIGENCE


␈↓ α∧␈↓␈↓ ¬kJohn McCarthy
␈↓ α∧␈↓␈↓ ∧←Computer Science Department
␈↓ α∧␈↓␈↓ ¬>Stanford University
␈↓ α∧␈↓␈↓ ∧wStanford, California 94305



␈↓ α∧␈↓␈↓αIntroduction␈↓

␈↓ α∧␈↓␈↓ αTIn␈α
(McCarthy␈α
and␈α
Hayes␈α
1969),␈α
we␈α
proposed␈α
dividing␈α
the␈α
artificial␈α
intelligence␈αproblem␈α
into
␈↓ α∧␈↓two␈α∩parts␈α⊃-␈α∩an␈α⊃epistemological␈α∩part␈α⊃and␈α∩a␈α⊃heuristic␈α∩part.␈α⊃ This␈α∩lecture␈α⊃further␈α∩explains␈α⊃this
␈↓ α∧␈↓division,␈α∪explains␈α∩some␈α∪of␈α∩the␈α∪epistemological␈α∩problems,␈α∪and␈α∩presents␈α∪some␈α∩new␈α∪results␈α∩and
␈↓ α∧␈↓approaches.

␈↓ α∧␈↓␈↓ αTThe␈αepistemological␈αpart␈αof␈αAI␈αstudies␈αwhat␈αkinds␈αof␈αfacts␈αabout␈αthe␈αworld␈αare␈αavailable␈αto
␈↓ α∧␈↓an␈α∩observer␈α∩with␈α∩given␈α⊃opportunities␈α∩to␈α∩observe,␈α∩how␈α∩these␈α⊃facts␈α∩can␈α∩be␈α∩represented␈α∩in␈α⊃the
␈↓ α∧␈↓memory␈αof␈αa␈α
computer,␈αand␈αwhat␈αrules␈α
permit␈αlegitimate␈αconclusions␈αto␈α
be␈αdrawn␈αfrom␈αthese␈α
facts.
␈↓ α∧␈↓It␈α
leaves␈α
aside␈α
the␈α
heuristic␈α
problems␈α
of␈α
how␈α
to␈α
search␈α
spaces␈α
of␈α
possibilities␈α
and␈α
how␈α
to␈α
match
␈↓ α∧␈↓patterns.

␈↓ α∧␈↓␈↓ αTConsidering epistemological problems separately has the following advantages:

␈↓ α∧␈↓␈↓ αT1.␈α
The␈α
same␈αproblems␈α
of␈α
what␈αinformation␈α
is␈α
available␈α
to␈αan␈α
observer␈α
and␈αwhat␈α
conclusions
␈↓ α∧␈↓can be drawn from information arise in connection with a variety of problem solving tasks.

␈↓ α∧␈↓␈↓ αT2.␈αA␈αsingle␈αsolution␈αof␈αthe␈αepistemological␈αproblems␈αcan␈αsupport␈αa␈αwide␈αvariety␈αof␈αheuristic
␈↓ α∧␈↓approaches to a problem.

␈↓ α∧␈↓␈↓ αT3.␈αAI␈αis␈αa␈αvery␈αdifficult␈αscientific␈αproblem,␈αso␈αthere␈αare␈αgreat␈αadvantages␈αin␈αfinding␈αparts␈αof
␈↓ α∧␈↓the problem that can be separated out and separately attacked.

␈↓ α∧␈↓␈↓ αT4.␈α⊂As␈α⊂the␈α⊂reader␈α⊂will␈α⊃see␈α⊂from␈α⊂the␈α⊂examples␈α⊂in␈α⊂the␈α⊃next␈α⊂section,␈α⊂it␈α⊂is␈α⊂quite␈α⊃difficult␈α⊂to
␈↓ α∧␈↓formalize␈α
the␈α
facts␈α
of␈α
common␈α
knowledge.␈α Existing␈α
programs␈α
that␈α
manipulate␈α
facts␈α
in␈α
some␈αof␈α
the
␈↓ α∧␈↓domains␈α∂are␈α∂confined␈α∂to␈α∂special␈α∂cases␈α∂and␈α∞don't␈α∂face␈α∂the␈α∂difficulties␈α∂that␈α∂must␈α∂be␈α∂overcome␈α∞to
␈↓ α∧␈↓achieve very intelligent behavior.

␈↓ α∧␈↓␈↓ αTWe␈α
have␈α
found␈α
first␈αorder␈α
logic␈α
to␈α
provide␈α
suitable␈αlanguages␈α
for␈α
expressing␈α
facts␈αabout␈α
the
␈↓ α∧␈↓world␈α⊗for␈α⊗epistemological␈α⊗research.␈α⊗ Recently␈α∃we␈α⊗have␈α⊗found␈α⊗that␈α⊗introducing␈α⊗concepts␈α∃as
␈↓ α∧␈↓individuals␈αmakes␈αpossible␈αa␈αfirst␈αorder␈αlogic␈αexpression␈αof␈αfacts␈αusually␈αexpressed␈αin␈αmodal␈αlogic
␈↓ α∧␈↓but with important advantages over modal logic - and so far no disadvantages.

␈↓ α∧␈↓␈↓ αTIn␈α
AI␈αliterature,␈α
the␈αterm␈α
␈↓↓predicate␈αcalculus␈↓␈α
is␈αusually␈α
extended␈αto␈α
cover␈αthe␈α
whole␈α
of␈αfirst
␈↓ α∧␈↓␈↓ u2


␈↓ α∧␈↓order␈α∪logic.␈α∀ While␈α∪predicate␈α∀calculus␈α∪includes␈α∪just␈α∀formulas␈α∪built␈α∀up␈α∪from␈α∀variables␈α∪using
␈↓ α∧␈↓predicate␈α⊃symbols,␈α⊂logical␈α⊃connectives,␈α⊂and␈α⊃quantifiers,␈α⊂first␈α⊃order␈α⊂logic␈α⊃also␈α⊂allows␈α⊃the␈α⊃use␈α⊂of
␈↓ α∧␈↓function␈αsymbols␈αto␈αform␈αterms␈αand␈αin␈αits␈αsemantics␈αinterprets␈αthe␈αequality␈αsymbol␈αas␈αstanding␈αfor
␈↓ α∧␈↓identity.␈α
 Our␈αfirst␈α
order␈α
systems␈αfurther␈α
use␈α
conditional␈αexpressions␈α
(non-recursive)␈α
to␈αform␈α
terms
␈↓ α∧␈↓and␈αλ-expressions␈αwith␈αindividuaal␈αvariables␈αto␈αform␈αnew␈αfunction␈αsymbols.␈α All␈αthese␈αextensions
␈↓ α∧␈↓are␈α
logically␈αinessential,␈α
because␈α
every␈αformula␈α
that␈α
includes␈αthem␈α
can␈α
be␈αreplaced␈α
by␈α
a␈αformula␈α
of
␈↓ α∧␈↓pure␈α
predicate␈α
calculus␈α
whose␈α
validity␈α
is␈α∞equivalent␈α
to␈α
it.␈α
 The␈α
extensions␈α
are␈α∞heuristically␈α
non-
␈↓ α∧␈↓trivial,␈α
because␈αthe␈α
equivalent␈α
predicate␈αcalculus␈α
may␈α
be␈αmuch␈α
longer␈α
and␈αis␈α
usually␈α
much␈αmore
␈↓ α∧␈↓difficult to understand - for man or machine.

␈↓ α∧␈↓␈↓ αTThe␈α
use␈αof␈α
first␈α
order␈αlogic␈α
in␈α
epistemological␈αresearch␈α
is␈α
a␈αseparate␈α
issue␈α
from␈αwhether␈α
first
␈↓ α∧␈↓order␈α∂sentences␈α∂are␈α∞appropriate␈α∂data␈α∂structures␈α∂for␈α∞representing␈α∂information␈α∂within␈α∂a␈α∞program.
␈↓ α∧␈↓As␈αto␈α
the␈αlatter,␈α
sentences␈αin␈α
logic␈αare␈α
at␈αone␈α
end␈αof␈α
a␈αspectrum␈α
of␈αrepresentations;␈α
they␈αare␈αeasy␈α
to
␈↓ α∧␈↓communicate,␈α∀have␈α∀logical␈α∀consequences␈α∀and␈α∀can␈α∪be␈α∀logical␈α∀consequences,␈α∀and␈α∀they␈α∀can␈α∪be
␈↓ α∧␈↓meaningful␈α
in␈α
a␈α
wide␈α
context.␈α
 Taking␈α
action␈α
on␈α
the␈α
basis␈α
of␈α
information␈α
stored␈α
as␈α
sentences,␈αis
␈↓ α∧␈↓slow␈α
and␈αthey␈α
are␈αnot␈α
the␈α
most␈αcompact␈α
representation␈αof␈α
information.␈α
 The␈αopposite␈α
extreme␈αis␈α
to
␈↓ α∧␈↓build␈α
the␈αinformation␈α
into␈αhardware,␈α
next␈αcomes␈α
building␈αit␈α
into␈αmachine␈α
language␈αprogram,␈α
then
␈↓ α∧␈↓a␈α⊗language␈α↔like␈α⊗LISP,␈α↔and␈α⊗then␈α⊗a␈α↔language␈α⊗like␈α↔MICROPLANNER,␈α⊗and␈α↔then␈α⊗perhaps
␈↓ α∧␈↓productions.␈α
 Compiling␈αor␈α
hardware␈αbuilding␈α
or␈α"automatic␈α
programming"␈αor␈α
just␈αplanning␈α
takes
␈↓ α∧␈↓information␈αfrom␈αa␈αmore␈αcontext␈αindependent␈αform␈αto␈αa␈αfaster␈αbut␈αmore␈αcontext␈αdependent␈αform.
␈↓ α∧␈↓A␈α∞clear␈α∞expression␈α
of␈α∞this␈α∞is␈α∞the␈α
transition␈α∞from␈α∞first␈α
order␈α∞logic␈α∞to␈α∞MICROPLANNER,␈α
where
␈↓ α∧␈↓much␈αinformation␈α
is␈αrepresented␈α
similarly␈αbut␈α
with␈αa␈α
specification␈αof␈α
how␈αthe␈α
information␈αis␈αto␈α
be
␈↓ α∧␈↓used.␈α∂ A␈α∂large␈α∂AI␈α∂system␈α∂should␈α⊂represent␈α∂some␈α∂information␈α∂as␈α∂first␈α∂order␈α∂logic␈α⊂sentences␈α∂and
␈↓ α∧␈↓other␈α∞information␈α∞should␈α∞be␈α∞compiled.␈α∞ In␈α∞fact,␈α∞it␈α∞will␈α∞often␈α∞be␈α∞necessary␈α∞to␈α∞represent␈α∂the␈α∞same
␈↓ α∧␈↓information␈αin␈αseveral␈αways.␈α Thus␈αa␈αball␈αplayer␈αhabit␈αof␈αkeeping␈αhis␈αeye␈αon␈αthe␈αball␈αis␈αbuilt␈αinto
␈↓ α∧␈↓his␈α∩"program",␈α∩but␈α∩it␈α∩is␈α∪also␈α∩explicitly␈α∩represented␈α∩as␈α∩a␈α∪sentence␈α∩so␈α∩that␈α∩the␈α∩advice␈α∪can␈α∩be
␈↓ α∧␈↓communicated.

␈↓ α∧␈↓␈↓ αTWhether␈αfirst␈αorder␈αlogic␈αmakes␈αa␈αgood␈αprogramming␈αlanguage␈αis␈αyet␈αanother␈αissue.␈α So␈αfar
␈↓ α∧␈↓it␈αseems␈α
to␈αhave␈αthe␈α
qualities␈αSamuel␈α
Johnson␈αascribed␈αto␈α
a␈αwoman␈αpreaching␈α
or␈αa␈α
dog␈αwalking
␈↓ α∧␈↓on␈αits␈αhind␈αlegs␈α-␈αone␈αis␈αsufficiently␈αimpressed␈αby␈αseeing␈αit␈αdone␈αat␈αall␈αthat␈αone␈αdoesn't␈αdemand␈αit
␈↓ α∧␈↓be done well.

␈↓ α∧␈↓␈↓ αTSuppose␈αwe␈αhave␈αa␈αtheory␈αof␈αa␈αcertain␈αclass␈αof␈αphenomena␈αaxiomatized␈αin␈α(say)␈αfirst␈αorder
␈↓ α∧␈↓logic.␈α⊂ We␈α⊃regard␈α⊂the␈α⊂theory␈α⊃as␈α⊂adequate␈α⊂for␈α⊃describing␈α⊂the␈α⊂epistemological␈α⊃aspects␈α⊂of␈α⊃a␈α⊂goal
␈↓ α∧␈↓seeking process involving these phenomena provided the following criterion is satisfied:

␈↓ α∧␈↓␈↓ αTImagine␈α∞a␈α∞robot␈α∞such␈α∞that␈α∞its␈α∞inputs␈α∞become␈α∞sentences␈α∞of␈α∞the␈α∞theory␈α∞stored␈α∞in␈α∞the␈α∞robot's
␈↓ α∧␈↓data-base,␈αand␈αsuch␈αthat␈αwhenever␈αa␈αsentence␈αof␈αthe␈αform␈α␈↓↓"I␈αshould␈αemit␈αoutput␈αX␈α
now"␈↓␈αappears
␈↓ α∧␈↓in␈α∞its␈α
data␈α∞base,␈α∞the␈α
robot␈α∞emits␈α∞output␈α
␈↓↓X.␈↓␈α∞Suppose␈α∞that␈α
new␈α∞sentences␈α∞appear␈α
in␈α∞its␈α∞data␈α
base
␈↓ α∧␈↓only␈α∩as␈α∩logical␈α∩consequences␈α∩of␈α∩sentences␈α∩already␈α⊃in␈α∩the␈α∩data␈α∩base.␈α∩ The␈α∩deduction␈α∩of␈α⊃these
␈↓ α∧␈↓sentences␈α⊂also␈α⊂use␈α⊃general␈α⊂sentences␈α⊂stored␈α⊃in␈α⊂the␈α⊂data␈α⊂base␈α⊃at␈α⊂the␈α⊂beginning␈α⊃constituting␈α⊂the
␈↓ α∧␈↓theory␈α∂being␈α∂tested.␈α∂ Usually␈α∞a␈α∂data-base␈α∂of␈α∂sentences␈α∞permits␈α∂many␈α∂different␈α∂deductions␈α∂to␈α∞be
␈↓ α∧␈↓made␈αso␈αthat␈αa␈αdeduction␈αprogram␈αwould␈αhave␈αto␈αchoose␈αwhich␈αdeduction␈αto␈αmake.␈α If␈αthere␈αwas
␈↓ α∧␈↓no␈α
program␈α∞that␈α
could␈α∞achieve␈α
the␈α
goal␈α∞by␈α
making␈α∞deductions␈α
allowed␈α
by␈α∞the␈α
theory␈α∞no␈α
matter
␈↓ α∧␈↓how␈αfast␈α
the␈αprogram␈αran,␈α
we␈αwould␈α
have␈αto␈αsay␈α
that␈αthe␈α
theory␈αwas␈αepistemologically␈α
inadequate.
␈↓ α∧␈↓A␈α
theory␈α
that␈α
was␈αepistemologically␈α
adequate␈α
would␈α
be␈αconsidered␈α
heuristically␈α
inadequate␈α
if␈αno
␈↓ α∧␈↓program␈αrunning␈αat␈α
a␈αreasonable␈αspeed␈α
with␈αany␈αrepresentation␈α
of␈αthe␈αfacts␈α
expressed␈αby␈αthe␈α
data
␈↓ α∧␈↓could␈α
do␈α
the␈α
job.␈α∞ We␈α
believe␈α
that␈α
most␈α∞present␈α
AI␈α
formalisms␈α
are␈α∞epistemologically␈α
inadequate
␈↓ α∧␈↓␈↓ u3


␈↓ α∧␈↓for␈α
general␈α
intelligence;␈α
i.e.␈α
they␈α
wouldn't␈α
achieve␈α
enough␈α
goals␈α
requiring␈α
general␈α∞intelligence␈α
no
␈↓ α∧␈↓matter␈αhow␈αfast␈αthey␈αwere␈αallowed␈αto␈αrun.␈α This␈αis␈αbecause␈αthe␈αepistemological␈αproblems␈αdiscussed
␈↓ α∧␈↓in the following sections haven't even been attacked yet.

␈↓ α∧␈↓␈↓ αTThe␈α
word␈α
"epistemology"␈α
is␈αused␈α
in␈α
this␈α
paper␈α
substantially␈αas␈α
many␈α
philosophers␈α
use␈αit,␈α
but
␈↓ α∧␈↓the␈α
problems␈α
considered␈α∞have␈α
a␈α
different␈α
emphasis.␈α∞ Philosophers␈α
emphasize␈α
what␈α∞is␈α
potentially
␈↓ α∧␈↓knowable␈α
with␈αmaximal␈α
opportunities␈αto␈α
observe␈αand␈α
compute,␈αwhereas␈α
AI␈αmust␈α
take␈αinto␈α
account
␈↓ α∧␈↓what␈αis␈αknowable␈αwith␈α
available␈αobservational␈αand␈αcomputational␈α
facilities.␈α Even␈αso,␈αmany␈αof␈α
the
␈↓ α∧␈↓same formalizations have both philosophical and AI interest.

␈↓ α∧␈↓␈↓ αTThe␈αsubsequent␈αsections␈αof␈αthis␈αpaper␈αlist␈αsome␈αepistemological␈αproblems,␈αdiscuss␈αsome␈αfirst
␈↓ α∧␈↓order␈αformalizations,␈α
introduce␈αconcepts␈α
as␈αobjects␈α
and␈αuse␈α
them␈αto␈α
express␈αfacts␈αabout␈α
knowledge,
␈↓ α∧␈↓describe␈α∀a␈α∀new␈α∀mode␈α∀of␈α∀reasoning␈α∀called␈α∀circumscription,␈α∀and␈α∀place␈α∀the␈α∀AI␈α∀problem␈α∀in␈α∪a
␈↓ α∧␈↓philosphical setting.



␈↓ α∧␈↓␈↓αEpistemological problems␈↓

␈↓ α∧␈↓␈↓ αTWe␈α
will␈αdiscuss␈α
what␈αfacts␈α
a␈α
person␈αor␈α
robot␈αmust␈α
take␈α
into␈αaccount␈α
in␈αorder␈α
to␈α
achieve␈αa
␈↓ α∧␈↓goal␈α
by␈αsome␈α
strategy␈α
of␈αaction.␈α
 We␈α
will␈αignore␈α
the␈αquestion␈α
of␈α
how␈αthese␈α
facts␈α
are␈αrepresented,
␈↓ α∧␈↓e.g.,␈αwhether␈αthey␈αare␈α
represented␈αby␈αsentences␈αfrom␈αwhich␈α
deductions␈αare␈αmade␈αor␈α
whether␈αthey
␈↓ α∧␈↓are␈αbuilt␈αinto␈αthe␈αprogram.␈α We␈αstart␈αwith␈αgreat␈αgenerality,␈αso␈αthere␈αmany␈αdifficulties.␈α We␈αobtain
␈↓ α∧␈↓successively␈αeasier␈αproblems␈αby␈α
assuming␈αthat␈αthe␈αdifficulties␈α
we␈αhave␈αrecognized␈αdon't␈αoccur␈α
until
␈↓ α∧␈↓we get to a class of problems we think we can solve.

␈↓ α∧␈↓␈↓ αT1.␈α⊂We␈α⊂begin␈α⊂by␈α⊂asking␈α⊂whether␈α⊂solving␈α⊂the␈α⊂problem␈α⊂requires␈α⊂the␈α⊂co-operation␈α⊂of␈α⊂other
␈↓ α∧␈↓people␈α⊂or␈α⊂overcoming␈α⊃their␈α⊂opposition.␈α⊂ If␈α⊂either␈α⊃is␈α⊂true,␈α⊂there␈α⊂are␈α⊃two␈α⊂subcases.␈α⊂ In␈α⊃the␈α⊂first
␈↓ α∧␈↓subcase,␈αthe␈αother␈αpeople's␈αdesires␈αand␈αgoals␈αmust␈αbe␈αtaken␈αinto␈αaccount,␈αand␈αthe␈αactions␈αthey␈αwill
␈↓ α∧␈↓take␈α
in␈α
given␈α
circumstances␈α
predicted␈αon␈α
the␈α
hypothesis␈α
that␈α
they␈αwill␈α
try␈α
to␈α
achieve␈α
their␈αgoals,
␈↓ α∧␈↓which␈αmay␈αhave␈αto␈αbe␈αdiscovered.␈α The␈αproblem␈αis␈αeven␈αmore␈αdifficult␈αif␈αbargaining␈αis␈αinvolved,
␈↓ α∧␈↓because␈αthen␈αthe␈αproblems␈αand␈αindeterminacies␈αof␈αgame␈αtheory␈αare␈αrelevant.␈α Even␈α
if␈αbargaining
␈↓ α∧␈↓is␈α
not␈αinvolved,␈α
the␈αrobot␈α
still␈αmust␈α
"put␈αhimself␈α
in␈αthe␈α
place␈αof␈α
the␈αother␈α
people␈αwith␈α
whom␈αhe
␈↓ α∧␈↓interacts".  Facts like a person wanting a thing or a person disliking another must be described.

␈↓ α∧␈↓␈↓ αTThe␈α∪second␈α∪subcase␈α∪makes␈α∪the␈α∪assumption␈α∪that␈α∪the␈α∪other␈α∪people␈α∪can␈α∪be␈α∪regarded␈α∩as
␈↓ α∧␈↓machines␈αwith␈αknown␈αinput-output␈αbehavior.␈α This␈αis␈αoften␈αa␈αgood␈αassumption,␈αe.g.,␈αone␈αassumes
␈↓ α∧␈↓that␈α∞a␈α∞clerk␈α∞in␈α∞a␈α∞store␈α∞will␈α∞sell␈α∞the␈α∞goods␈α∞in␈α∞exchange␈α∞for␈α∞their␈α∞price␈α∞and␈α∞that␈α∞a␈α∂professor␈α∞will
␈↓ α∧␈↓assign␈αa␈αgrade␈αin␈αaccordance␈αwith␈αthe␈αquality␈αof␈αthe␈αwork␈αdone.␈α Neither␈αthe␈αgoals␈αof␈αthe␈αclerk␈αor
␈↓ α∧␈↓the␈α∂professor␈α⊂need␈α∂be␈α∂taken␈α⊂into␈α∂account;␈α⊂either␈α∂might␈α∂well␈α⊂regard␈α∂an␈α∂attempt␈α⊂to␈α∂use␈α⊂them␈α∂to
␈↓ α∧␈↓optimize␈αthe␈αinteraction␈αas␈αan␈αinvasion␈αof␈αprivacy.␈α In␈αsuch␈αcircumstances,␈αman␈αusually␈αprefers␈αto
␈↓ α∧␈↓be regarded as a machine.

␈↓ α∧␈↓␈↓ αTLet␈α∞us␈α
now␈α∞suppose␈α
that␈α∞either␈α
other␈α∞people␈α∞are␈α
not␈α∞involved␈α
in␈α∞the␈α
problem␈α∞or␈α∞that␈α
the
␈↓ α∧␈↓information␈α
available␈α∞about␈α
their␈α
actions␈α∞takes␈α
the␈α∞form␈α
of␈α
input-output␈α∞relations␈α
and␈α∞does␈α
not
␈↓ α∧␈↓involve understanding their goals.

␈↓ α∧␈↓␈↓ αT2.␈αThe␈αsecond␈α
question␈αis␈αwhether␈α
the␈αstrategy␈αinvolves␈α
the␈αacquisition␈αof␈αknowledge.␈α
 Even
␈↓ α∧␈↓if␈α∂we␈α∂can␈α∂treat␈α∂other␈α∂people␈α∂as␈α∂machines,␈α∂we␈α∂still␈α∂may␈α∂have␈α∂to␈α∂reason␈α∂about␈α∂what␈α⊂they␈α∂know.
␈↓ α∧␈↓␈↓ u4


␈↓ α∧␈↓Thus␈αan␈α
airline␈αclerk␈αknows␈α
what␈αairplanes␈αfly␈α
from␈αhere␈αto␈α
there␈αand␈αwhen,␈α
although␈αhe␈αwill␈α
tell
␈↓ α∧␈↓you␈α∞when␈α∞asked␈α∞without␈α
your␈α∞having␈α∞to␈α∞motivate␈α∞him.␈α
 One␈α∞must␈α∞also␈α∞consider␈α∞information␈α
in
␈↓ α∧␈↓books and in tables.  The latter information is described by other information.

␈↓ α∧␈↓␈↓ αTThe␈αsecond␈αsubcase␈αof␈αknowledge␈αis␈αaccording␈αto␈αwhether␈αthe␈αinformation␈αobtained␈αcan␈αbe
␈↓ α∧␈↓simply␈α
plugged␈α
into␈α
a␈α
program␈α
or␈α
whether␈α
it␈α
enters␈α
in␈α
a␈α
more␈α
complex␈α
way.␈α
 Thus␈α
if␈α∞the␈α
robot
␈↓ α∧␈↓must␈αtelephone␈α
someone,␈αits␈α
program␈αcan␈αsimply␈α
dial␈αthe␈α
number␈αobtained,␈αbut␈α
it␈αmight␈α
have␈αto
␈↓ α∧␈↓ask␈α
a␈α
question,␈α
␈↓↓"How␈α
can␈α
I␈α
get␈α
in␈α
touch␈α
with␈α
Mike?"␈↓␈α
and␈α
reason␈α
about␈α
how␈α
to␈α
use␈α∞the␈α
resulting
␈↓ α∧␈↓information␈αin␈αconjunction␈αwith␈αother␈αinformation.␈α The␈αgeneral␈αdistinction␈αmay␈αbe␈α
according␈αto
␈↓ α∧␈↓whether new sentences are generated or whether values are just assigned to variables.

␈↓ α∧␈↓␈↓ αTAn␈α
example␈α
worth␈α∞considering␈α
is␈α
that␈α∞a␈α
sophisticated␈α
air␈α
traveler␈α∞rarely␈α
asks␈α
how␈α∞he␈α
will
␈↓ α∧␈↓get␈α∞from␈α
the␈α∞arriving␈α
flight␈α∞to␈α
the␈α∞departing␈α
flight␈α∞at␈α
an␈α∞airport␈α
where␈α∞he␈α
must␈α∞change␈α
planes.
␈↓ α∧␈↓He␈αis␈αconfident␈α
that␈αthe␈αinformation␈α
will␈αbe␈αavailable␈α
in␈αa␈αform␈α
he␈αcan␈αunderstand␈α
at␈αthe␈αtime␈α
he
␈↓ α∧␈↓will need it.

␈↓ α∧␈↓␈↓ αTIf␈α
the␈α
strategy␈α
is␈α
embodied␈α
in␈α
a␈α
program␈α
that␈α
branches␈α
on␈α
an␈α
environmental␈α
condition␈αor
␈↓ α∧␈↓reads␈αa␈αnumerical␈αparameter␈αfrom␈αthe␈αenvironment,␈αwe␈αcan␈αregard␈αit␈αas␈αobtaining␈αknowledge,␈αbut
␈↓ α∧␈↓this is obviously an easier case than those we have discussed.

␈↓ α∧␈↓␈↓ αT3.␈α∂A␈α∂problem␈α∂is␈α∂more␈α∂difficult␈α∂if␈α∂it␈α∂involves␈α∂concurrent␈α∂events␈α∂and␈α∂actions.␈α∂ To␈α⊂me␈α∂this
␈↓ α∧␈↓seems␈α
to␈αbe␈α
the␈αmost␈α
difficult␈αunsolved␈α
epistemological␈α
problem␈αfor␈α
AI␈α-␈α
how␈αto␈α
express␈αrules␈α
that
␈↓ α∧␈↓give␈α
the␈α
effects␈α
of␈α
actions␈α
and␈α
events␈α∞when␈α
they␈α
occur␈α
concurrently.␈α
 We␈α
may␈α
contrast␈α∞this␈α
with
␈↓ α∧␈↓the sequential case treated in (McCarthy and Hayes 1969).  In the sequential case we c→n write

␈↓ α∧␈↓1)␈↓ αt ␈↓↓s' = result(e,s)␈↓

␈↓ α∧␈↓where␈α␈↓↓s'␈↓␈α
is␈αthe␈αsituation␈α
that␈αresults␈αwhen␈α
event␈α␈↓↓e␈↓␈α
occurs␈αin␈αsituation␈α
␈↓↓s␈↓.␈α The␈αeffects␈α
of␈α␈↓↓e␈↓␈α
can␈αbe
␈↓ α∧␈↓described␈αby␈αsentences␈αrelating␈α␈↓↓s',␈↓␈α
␈↓↓e␈↓␈αand␈α␈↓↓s.␈↓␈αOne␈αcan␈α
attempt␈αa␈αsimilar␈αformalism␈αgiving␈αa␈α
␈↓↓partial
␈↓ α∧␈↓↓situation␈↓␈α
that␈α
results␈α
from␈α
an␈α∞event␈α
in␈α
another␈α
partial␈α
situation,␈α
but␈α∞it␈α
is␈α
difficult␈α
to␈α
see␈α∞how␈α
to
␈↓ α∧␈↓apply this to cases in which other events may affect with the occurrence.

␈↓ α∧␈↓␈↓ αTWhen␈αevents␈αare␈αconcurrent,␈αit␈αis␈αusually␈αnecessary␈αto␈αregard␈αtime␈αas␈αcontinuous.␈α We␈αhave
␈↓ α∧␈↓events␈α
like␈α
␈↓↓raining␈α
until␈α
the␈α
reservoir␈α
overflows␈↓␈α∞and␈α
questions␈α
like␈α
␈↓↓Where␈α
was␈α
his␈α
train␈α∞when␈α
we
␈↓ α∧␈↓↓wanted to call him?␈↓.

␈↓ α∧␈↓␈↓ αTComputer␈α
science␈αhas␈α
recently␈α
begun␈αto␈α
formalize␈αparallel␈α
processes␈α
so␈αthat␈α
it␈α
is␈αsometimes
␈↓ α∧␈↓possible␈α∂to␈α∂prove␈α⊂that␈α∂a␈α∂system␈α⊂of␈α∂parallel␈α∂processes␈α∂will␈α⊂meet␈α∂its␈α∂specifications.␈α⊂ However,␈α∂the
␈↓ α∧␈↓knowledge␈α
available␈α
to␈α
a␈α
robot␈αof␈α
the␈α
other␈α
processes␈α
going␈α
on␈αin␈α
the␈α
world␈α
will␈α
rarely␈α
take␈αthe
␈↓ α∧␈↓form␈α
of␈α
a␈α
Petri␈α
net␈αor␈α
any␈α
of␈α
the␈α
other␈α
formalisms␈αused␈α
in␈α
engineering␈α
or␈α
computer␈α
science.␈α In
␈↓ α∧␈↓fact,␈α∞anyone␈α∞who␈α∂wishes␈α∞to␈α∞prove␈α∞correct␈α∂an␈α∞airline␈α∞reservation␈α∞system␈α∂or␈α∞an␈α∞air␈α∂traffic␈α∞control
␈↓ α∧␈↓system␈αmust␈αuse␈αinformation␈αabout␈αthe␈αbehavior␈αof␈αthe␈αexternal␈αworld␈αthat␈αis␈αless␈αspecific␈αthan␈αa
␈↓ α∧␈↓program.␈α∩ Nevertheless,␈α∩the␈α∩formalisms␈α∩for␈α∩expressing␈α∩facts␈α∩about␈α∩parallel␈α∩and␈α∩indeterminate
␈↓ α∧␈↓programs provide a start for axiomatizing concurrent action.

␈↓ α∧␈↓␈↓ αT4.␈α∞A␈α
robot␈α∞must␈α
be␈α∞able␈α
to␈α∞express␈α
knowledge␈α∞about␈α
space,␈α∞and␈α
the␈α∞locations,␈α∞shapes␈α
and
␈↓ α∧␈↓layouts␈αof␈αobjects␈α
in␈αspace.␈α Present␈α
programs␈αtreat␈αonly␈αvery␈α
special␈αcases.␈α Usually␈α
locations␈αare
␈↓ α∧␈↓discrete␈α-␈αblock␈αA␈αmay␈αbe␈αon␈αblock␈αB␈αbut␈αthe␈αformalisms␈αdo␈αnot␈αallow␈αanything␈αto␈αbe␈αsaid␈αabout
␈↓ α∧␈↓where␈α⊂on␈α∂block␈α⊂B␈α∂it␈α⊂is,␈α⊂and␈α∂what␈α⊂shape␈α∂space␈α⊂is␈α∂left␈α⊂on␈α⊂block␈α∂B␈α⊂for␈α∂placing␈α⊂other␈α⊂blocks␈α∂or
␈↓ α∧␈↓␈↓ u5


␈↓ α∧␈↓whether␈αblock␈αA␈αcould␈αbe␈αmoved␈αto␈αproject␈αout␈αa␈αbit␈αin␈αorder␈αto␈αplace␈αanother␈αblock.␈α A␈αfew␈αare
␈↓ α∧␈↓more␈α
sophisticated,␈α
but␈α
the␈α
objects␈α
must␈α
have␈α
simple␈α
geometric␈α
shapes.␈α
 A␈α
formalism␈α
capable␈α
of
␈↓ α∧␈↓representing␈α
the␈α
geometric␈α
information␈α
people␈α
get␈α
from␈α
seeing␈α
and␈α
handling␈α
objects␈α
has␈α
not,␈αto␈α
my
␈↓ α∧␈↓knowledge, been approached.

␈↓ α∧␈↓␈↓ αTThe␈α∀difficulty␈α∀in␈α∀expressing␈α∀such␈α∀facts␈α∪is␈α∀indicated␈α∀by␈α∀the␈α∀limitations␈α∀of␈α∀English␈α∪in
␈↓ α∧␈↓expressing␈α∩human␈α∩visual␈α∩knowledge.␈α∩ We␈α∪can␈α∩describe␈α∩regular␈α∩geometric␈α∩shapes␈α∪precisely␈α∩in
␈↓ α∧␈↓English␈α∞(fortified␈α∞by␈α∞mathematics),␈α
but␈α∞the␈α∞information␈α∞we␈α
use␈α∞for␈α∞recognizing␈α∞another␈α
person's
␈↓ α∧␈↓face␈α⊂cannot␈α⊂ordinarily␈α⊂be␈α⊃transmitted␈α⊂in␈α⊂words.␈α⊂ We␈α⊂can␈α⊃answer␈α⊂many␈α⊂more␈α⊂questions␈α⊃in␈α⊂the
␈↓ α∧␈↓presence of a scene than we can from memory.

␈↓ α∧␈↓␈↓ αT5.␈α⊂The␈α⊃relation␈α⊂between␈α⊂three␈α⊃dimensional␈α⊂objects␈α⊂and␈α⊃their␈α⊂two␈α⊂dimensional␈α⊃retinal␈α⊂or
␈↓ α∧␈↓camera␈α_images␈α_is␈α_mostly␈α_untreated.␈α_ Contrary␈α_to␈α_some␈α_philosophical␈α_positions,␈α_the␈α_three
␈↓ α∧␈↓dimensional␈α
object␈α∞is␈α
treated␈α∞by␈α
our␈α∞minds␈α
as␈α
distinct␈α∞from␈α
its␈α∞appearances.␈α
 People␈α∞blind␈α
from
␈↓ α∧␈↓birth␈α⊃can␈α⊃still␈α⊃communicate␈α⊃in␈α⊃the␈α⊃same␈α⊃language␈α⊃as␈α⊃sighted␈α⊃people␈α⊃about␈α⊃three␈α⊃dimensional
␈↓ α∧␈↓objects.␈α
 We␈α
need␈α
a␈α
formalism␈α
that␈α
treats␈α
three␈α
dimensional␈α
objects␈α
as␈α
instances␈α
of␈α
patterns␈α
and
␈↓ α∧␈↓their␈α⊃two␈α⊃dimensional␈α∩appearances␈α⊃as␈α⊃projections␈α⊃of␈α∩these␈α⊃patterns␈α⊃modified␈α⊃by␈α∩lighting␈α⊃and
␈↓ α∧␈↓occlusion.

␈↓ α∧␈↓␈↓ αT6.␈α∞Objects␈α
can␈α∞be␈α
made␈α∞by␈α∞shaping␈α
materials␈α∞and␈α
by␈α∞combining␈α
other␈α∞objects.␈α∞ They␈α
can
␈↓ α∧␈↓also␈α∩be␈α∩taken␈α⊃apart,␈α∩cut␈α∩apart␈α∩or␈α⊃destroyed␈α∩in␈α∩various␈α∩ways.␈α⊃ What␈α∩people␈α∩know␈α∩about␈α⊃the
␈↓ α∧␈↓relations between materials and objects remains to be described.

␈↓ α∧␈↓␈↓ αT7.␈α∞Modal␈α∞concepts␈α∞like␈α∞␈↓↓event␈α∞e1␈α∞caused␈α∞event␈α
e2␈↓␈α∞and␈α∞␈↓↓person␈α∞e␈α∞can␈α∞do␈α∞action␈α∞a␈↓␈α∞are␈α
needed.
␈↓ α∧␈↓(McCarthy␈αand␈αHayes␈α1969)␈αregards␈αability␈αas␈αa␈α
function␈αof␈αa␈αperson's␈αposition␈αin␈αa␈αcausal␈α
system
␈↓ α∧␈↓and␈αnot␈α
at␈αall␈αas␈α
a␈αfunction␈α
of␈αhis␈αinternal␈α
structure.␈α This␈α
still␈αseems␈αcorrect,␈α
but␈αthat␈αtreatment␈α
is
␈↓ α∧␈↓only␈α⊂metaphysically␈α⊂adequate,␈α⊂because␈α⊂it␈α∂doesn't␈α⊂provide␈α⊂for␈α⊂expressing␈α⊂the␈α⊂information␈α∂about
␈↓ α∧␈↓ability that people actually have.

␈↓ α∧␈↓␈↓ αT8.␈α⊃Suppose␈α⊃now␈α⊃that␈α⊃the␈α⊃problem␈α⊃can␈α∩be␈α⊃formalized␈α⊃in␈α⊃terms␈α⊃of␈α⊃a␈α⊃single␈α⊃state␈α∩that␈α⊃is
␈↓ α∧␈↓changed␈α∩by␈α∩events.␈α∩ In␈α∩interesting␈α⊃cases,␈α∩the␈α∩set␈α∩of␈α∩components␈α⊃of␈α∩the␈α∩state␈α∩depends␈α∩on␈α⊃the
␈↓ α∧␈↓problem,␈α
but␈α
common␈αgeneral␈α
knowledge␈α
is␈α
usually␈αexpressed␈α
in␈α
terms␈α
of␈αthe␈α
effect␈α
of␈α
an␈αaction
␈↓ α∧␈↓on␈α
one␈α
or␈α
a␈α
few␈α
components␈α
of␈α
the␈α
state.␈α
 However,␈α
it␈α
cannot␈α
always␈α
be␈α
assumed␈α
that␈α∞the␈α
other
␈↓ α∧␈↓components␈α⊃are␈α⊃unchanged,␈α⊃especially␈α⊃because␈α⊃the␈α⊃state␈α⊂can␈α⊃be␈α⊃described␈α⊃in␈α⊃a␈α⊃variety␈α⊃of␈α⊂co-
␈↓ α∧␈↓ordinate␈α∞systems␈α
and␈α∞the␈α
meaning␈α∞of␈α
changing␈α∞a␈α
single␈α∞co-ordinate␈α
depends␈α∞on␈α∞the␈α
co-ordinate
␈↓ α∧␈↓system.␈α The␈αproblem␈αof␈αexpressing␈αinformation␈αabout␈αwhat␈αremains␈αunchanged␈αby␈αan␈αevent␈αwas
␈↓ α∧␈↓called␈α
␈↓↓the␈α
frame␈α
problem␈↓␈α
in␈α
(McCarthy␈α
and␈α
Hayes␈α
1969).␈α
 Minsky␈α
subsequently␈α
confused␈αmatters
␈↓ α∧␈↓by␈α∞using␈α
the␈α∞word␈α∞"frame"␈α
for␈α∞patterns␈α
into␈α∞which␈α∞situations␈α
may␈α∞fit.␈α
 (His␈α∞hypothesis␈α∞seems␈α
to
␈↓ α∧␈↓have␈α⊃been␈α⊃that␈α⊃almost␈α∩all␈α⊃situations␈α⊃encountered␈α⊃in␈α⊃human␈α∩problem␈α⊃solving␈α⊃fit␈α⊃into␈α∩a␈α⊃small
␈↓ α∧␈↓number␈αof␈αpreviously␈αknown␈αpatterns␈αof␈αsituation␈αand␈αgoal.␈α I␈αregard␈αthis␈αas␈αunlikely␈αin␈αdifficult
␈↓ α∧␈↓problems).

␈↓ α∧␈↓␈↓ αT9.␈α∞The␈α∂␈↓↓frame␈α∞problem␈↓␈α∞may␈α∂be␈α∞a␈α∂subcase␈α∞of␈α∞what␈α∂we␈α∞call␈α∞the␈α∂␈↓↓qualification␈α∞problem␈↓,␈α∂and␈α∞a
␈↓ α∧␈↓good␈αsolution␈αof␈αthe␈αqualification␈αproblem␈αmay␈αsolve␈αthe␈αframe␈αproblem␈αalso.␈α In␈αthe␈α␈↓↓missionaries
␈↓ α∧␈↓↓and␈α
cannibals␈↓␈α
problem,␈α
a␈α
boat␈α
holding␈α
two␈α
people␈α
is␈α
stated␈α
to␈α
be␈α
available.␈α
 In␈α
the␈α
statement␈α
of␈α
the
␈↓ α∧␈↓problem,␈α
nothing␈α
is␈αsaid␈α
about␈α
how␈αboats␈α
are␈α
used␈αto␈α
cross␈α
rivers,␈αso␈α
obviously␈α
this␈αinformation
␈↓ α∧␈↓must␈α∂come␈α∂from␈α∞common␈α∂knowledge,␈α∂and␈α∞a␈α∂computer␈α∂program␈α∞capable␈α∂of␈α∂solving␈α∂the␈α∞problem
␈↓ α∧␈↓from␈α∂an␈α∞English␈α∂description␈α∂or␈α∞from␈α∂a␈α∞translation␈α∂of␈α∂this␈α∞description␈α∂into␈α∞logic␈α∂must␈α∂have␈α∞the
␈↓ α∧␈↓requisite␈αcommon␈αknowledge.␈α The␈αsimplest␈αstatement␈αabout␈αthe␈αuse␈αof␈αboats␈αsays␈αsomething␈αlike,
␈↓ α∧␈↓␈↓ u6


␈↓ α∧␈↓␈↓↓"If␈α
a␈α
boat␈α
is␈α
at␈α
one␈α
point␈α
on␈α
the␈α
shore␈α
of␈α
a␈α
body␈α
of␈α
water,␈α
and␈α
a␈α
set␈α
of␈α
things␈α
enter␈α
the␈α
boat,␈αand␈α
the
␈↓ α∧␈↓↓boat␈α
is␈α
propelled␈αto␈α
the␈α
another␈αpoint␈α
on␈α
the␈αshore,␈α
and␈α
the␈α
things␈αexit␈α
the␈α
boat,␈αthen␈α
they␈α
will␈αbe␈α
at
␈↓ α∧␈↓↓the␈αsecond␈αpoint␈α
on␈αthe␈αshore"␈↓.␈α
 However,␈αthis␈αstatement␈αis␈α
too␈αrigid␈αto␈α
be␈αtrue,␈αbecause␈αanyone␈α
will
␈↓ α∧␈↓admit␈α∞that␈α∞if␈α∂the␈α∞boat␈α∞is␈α∞a␈α∂rowboat␈α∞and␈α∞has␈α∞a␈α∂leak␈α∞or␈α∞no␈α∞oars,␈α∂the␈α∞action␈α∞may␈α∞not␈α∂achieve␈α∞its
␈↓ α∧␈↓intended␈αresult.␈α One␈αmight␈αtry␈αamending␈αthe␈αcommon␈αknowledge␈αstatement␈αabout␈αboats,␈αbut␈αthis
␈↓ α∧␈↓encounters␈α
difficulties␈α
when␈α
a␈αcritic␈α
demands␈α
a␈α
qualification␈α
that␈αthe␈α
vertical␈α
exhaust␈α
stack␈α
of␈αa
␈↓ α∧␈↓diesel␈α
boat␈α
must␈α
not␈α
be␈α
struck␈α
square␈α
by␈α
a␈α
cow␈α
turd␈α
dropped␈α
by␈α
a␈α
passing␈α
hawk␈α
or␈α
some␈α
other
␈↓ α∧␈↓event␈α
that␈α
no-one␈αhas␈α
previously␈α
thought␈α
of.␈α We␈α
need␈α
to␈α
be␈αable␈α
to␈α
say␈α
that␈αthe␈α
boat␈α
can␈αbe␈α
used
␈↓ α∧␈↓as␈αa␈αvehicle␈αfor␈αcrossing␈αa␈αbody␈αof␈α
water␈αunless␈αsomething␈αprevents␈αit.␈α However,␈αsince␈αwe␈αare␈α
not
␈↓ α∧␈↓willing␈αto␈αdelimit␈αin␈αadvance␈αpossible␈αcircumstances␈αthat␈αmay␈αprevent␈αthe␈αuse␈αof␈αthe␈αboat,␈αthere␈αis
␈↓ α∧␈↓still␈α
a␈α
problem␈α
of␈αproving␈α
or␈α
at␈α
least␈αconjecturing␈α
that␈α
nothing␈α
prevents␈αthe␈α
use␈α
of␈α
the␈α
boat.␈α A
␈↓ α∧␈↓method␈α
of␈α
reasoning␈α
called␈α∞␈↓↓circumscription␈↓,␈α
described␈α
in␈α
a␈α
subsequent␈α∞section␈α
of␈α
this␈α
paper,␈α∞is␈α
a
␈↓ α∧␈↓candidate␈α⊃for␈α⊂solving␈α⊃the␈α⊂qualification␈α⊃problem.␈α⊂ The␈α⊃reduction␈α⊂of␈α⊃the␈α⊂frame␈α⊃problem␈α⊃to␈α⊂the
␈↓ α∧␈↓qualification problem has not been fully carried out, however.



␈↓ α∧␈↓␈↓αCircumscription - a way of jumping to conclusions␈↓

␈↓ α∧␈↓␈↓ αTThere␈α
is␈αan␈α
intuition␈α
that␈αnot␈α
all␈α
human␈αreasoning␈α
can␈α
be␈αtranslated␈α
into␈α
deduction␈αin␈α
some
␈↓ α∧␈↓formal␈α∂system␈α∂of␈α⊂mathematical␈α∂logic,␈α∂and␈α⊂therefore␈α∂mathematical␈α∂logic␈α⊂should␈α∂be␈α∂rejected␈α⊂as␈α∂a
␈↓ α∧␈↓formalism␈α⊂for␈α⊂expressing␈α⊂what␈α⊂a␈α⊂robot␈α⊂should␈α⊂know␈α⊂about␈α⊂the␈α⊂world.␈α⊂ The␈α⊂intuition␈α⊂in␈α∂itself
␈↓ α∧␈↓doesn't carry a convincing idea of what is lacking and how it might be supplied.

␈↓ α∧␈↓␈↓ αTWe␈α⊂can␈α⊂confirm␈α⊂part␈α∂of␈α⊂the␈α⊂intuition␈α⊂by␈α∂describing␈α⊂a␈α⊂previously␈α⊂unformalized␈α⊂mode␈α∂of
␈↓ α∧␈↓reasoning␈α∩called␈α∩␈↓↓circumscription␈↓,␈α∩which␈α∩we␈α∩can␈α∩show␈α∩does␈α∩not␈α∩correspond␈α∩to␈α∩deduction␈α∪in␈α∩a
␈↓ α∧␈↓mathematical␈αsystem.␈α The␈αconclusions␈αit␈αyields␈αare␈αjust␈αconjectures␈αand␈αsometimes␈αeven␈αintroduce
␈↓ α∧␈↓inconsistency.␈α∞ We␈α
will␈α∞argue␈α
that␈α∞humans␈α
often␈α∞use␈α
circumscription,␈α∞and␈α
robots␈α∞must␈α∞too.␈α
 The
␈↓ α∧␈↓second␈α
part␈α
of␈α
the␈α
intuition␈α-␈α
the␈α
rejection␈α
of␈α
mathematical␈α
logic␈α-␈α
is␈α
not␈α
confirmed;␈α
the␈αnew␈α
mode
␈↓ α∧␈↓of␈α∩reasoning␈α∩is␈α⊃best␈α∩understood␈α∩and␈α⊃used␈α∩within␈α∩a␈α⊃mathematical␈α∩logical␈α∩framework␈α∩and␈α⊃co-
␈↓ α∧␈↓ordinates␈α
well␈α
with␈α
mathematical␈α
logical␈α
deduction.␈α
 We␈α
think␈α
␈↓↓circumscription␈↓␈α
accounts␈α
for␈α
some␈α
of
␈↓ α∧␈↓the successes and some of the errors of human reasoning.

␈↓ α∧␈↓␈↓ αTThe␈α
intuitive␈α
idea␈αof␈α
␈↓↓circumscription␈↓␈α
is␈α
as␈αfollows:␈α
We␈α
know␈α
some␈αobjects␈α
in␈α
a␈α
given␈αclass
␈↓ α∧␈↓and␈α
we␈α
have␈α
some␈α∞ways␈α
of␈α
generating␈α
more.␈α∞ We␈α
jump␈α
to␈α
the␈α∞conclusion␈α
that␈α
this␈α
gives␈α∞all␈α
the
␈↓ α∧␈↓objects in the class.  Thus we ␈↓↓circumscribe␈↓ the class to the objects we know how to generate.

␈↓ α∧␈↓␈↓ αTFor␈αexample,␈αsuppose␈αthat␈αobjects␈α␈↓↓a,␈↓␈α␈↓↓b␈↓␈αand␈α␈↓↓c␈↓␈αsatisfy␈αthe␈αpredicate␈α␈↓↓P␈↓␈αand␈αthat␈αthe␈αfunctions
␈↓ α∧␈↓␈↓↓f(x)␈↓␈α∞and␈α∞␈↓↓g(x,y)␈↓␈α∞take␈α∞arguments␈α∞satisfying␈α∞␈↓↓P␈↓␈α
into␈α∞values␈α∞also␈α∞satisfying␈α∞␈↓↓P.␈↓␈α∞The␈α∞first␈α∞order␈α
logic
␈↓ α∧␈↓expression of these facts is

␈↓ α∧␈↓2)␈↓ αt ␈↓↓P(a) ∧ P(b) ∧ P(c) ∧ (∀x)(P(x) ⊃ P(f(x))) ∧ (∀x y)(P(x) ∧ P(y) ⊃ P(g(x,y)))␈↓.

␈↓ α∧␈↓The␈αconjecture␈αthat␈αeverything␈αsatisfying␈α␈↓↓P␈↓␈αis␈αgenerated␈αfrom␈α␈↓↓a,␈↓␈α␈↓↓b␈↓␈αand␈α␈↓↓c␈↓␈αby␈αrepeated␈αapplication
␈↓ α∧␈↓of the functions ␈↓↓f␈↓ and ␈↓↓g␈↓ is expressed by the sentence schema

␈↓ α∧␈↓3)␈↓ αt␈α
␈↓↓␈↓	F␈↓↓(a)␈α∧␈α
␈↓	F␈↓↓(b)␈α∧␈α
␈↓	F␈↓↓(c)␈α∧␈α
(∀x)(␈↓	F␈↓↓(x)␈α⊃␈α
␈↓	F␈↓↓(f(x)))␈α∧␈α
(∀x␈αy)(␈↓	F␈↓↓(x)␈α
∧␈α␈↓	F␈↓↓(y)␈α
⊃␈α␈↓	F␈↓↓(g(x,y)))␈α
⊃␈α
(∀x)(P(x)␈α⊃
␈↓ α∧␈↓↓␈↓	F␈↓↓(x))␈↓,

␈↓ α∧␈↓where ␈↓	F␈↓ is a free predicate variable for which any predicate may be substituted.
␈↓ α∧␈↓␈↓ u7


␈↓ α∧␈↓It␈αis␈αonly␈αa␈αconjecture,␈αbecause␈αthere␈αmight␈αbe␈αan␈αobject␈α␈↓↓d␈↓␈αsuch␈αthat␈α␈↓↓P(d)␈↓␈αwhich␈αis␈αnot␈αgenerated
␈↓ α∧␈↓in␈αthis␈αway.␈α (3)␈α
is␈αone␈αway␈αof␈α
writing␈α␈↓↓the␈αcircumscription␈↓␈αof␈α
(2).␈α The␈αheuristics␈αof␈α
circumscription
␈↓ α∧␈↓-␈αwhen␈αone␈αcan␈αplausibly␈αconjecture␈αthat␈αthe␈αobjects␈αgenerated␈αin␈αknown␈αways␈αare␈αall␈αthere␈αare␈α-
␈↓ α∧␈↓are completely unstudied.

␈↓ α∧␈↓␈↓ αTCircumscription␈α⊃is␈α⊃not␈α⊃deduction␈α⊃in␈α⊃disguise,␈α⊂because␈α⊃every␈α⊃form␈α⊃of␈α⊃deduction␈α⊃has␈α⊂two
␈↓ α∧␈↓properties␈α
that␈α
circumscription␈α
lacks␈α
-␈αtransitivity␈α
and␈α
what␈α
we␈α
may␈α
call␈α␈↓↓monotonicity␈↓.␈α
 Transitivity
␈↓ α∧␈↓says␈α∞that␈α∂if␈α∞␈↓↓p ␈↓πr␈↓↓ r␈↓␈α∂and␈α∞␈↓↓r ␈↓πr␈↓↓ s␈↓,␈α∂then␈α∞␈↓↓p ␈↓πr␈↓↓ s␈↓.␈α∂ Monotonicity␈α∞says␈α∞that␈α∂if␈α∞␈↓↓A ␈↓πr␈↓↓ p␈↓␈α∂(where␈α∞␈↓↓A␈↓␈α∂is␈α∞a␈α∂set␈α∞of
␈↓ α∧␈↓sentences)␈α∀and␈α∪␈↓↓A ⊂ B␈↓,␈α∀then␈α∀␈↓↓B ␈↓πr␈↓↓ p␈↓␈α∪for␈α∀deduction.␈α∀ Intuitively,␈α∪circumscription␈α∀should␈α∀not␈α∪be
␈↓ α∧␈↓monotonic,␈α
since␈α
it␈α
is␈α
the␈α
conjecture␈α
that␈α
the␈αways␈α
we␈α
know␈α
of␈α
generating␈α
␈↓↓P␈↓'s␈α
are␈α
all␈α
there␈αare.␈α
 An
␈↓ α∧␈↓enlarged set ␈↓↓B␈↓ of sentences may contain a new way of generating ␈↓↓P␈↓'s.

␈↓ α∧␈↓␈↓ αTIf␈α⊂we␈α∂use␈α⊂second␈α⊂order␈α∂logic␈α⊂or␈α∂the␈α⊂language␈α⊂of␈α∂set␈α⊂theory,␈α∂then␈α⊂circumscription␈α⊂can␈α∂be
␈↓ α∧␈↓expressed as a sentence rather than as a schema.  In set theory it becomes.

␈↓ α∧␈↓3')␈α␈↓↓(∀␈↓	F␈↓↓)(a␈αε␈α␈↓	F␈↓↓␈α∧␈αb␈αε␈α␈↓	F␈↓↓␈α∧␈αc␈αε␈α␈↓	F␈↓↓␈α∧␈α(∀x)(x␈αε␈α␈↓	F␈↓↓␈α⊃␈αf(x)␈αε␈α␈↓	F␈↓↓)␈α∧␈α(∀x␈αy)(x␈αε␈α␈↓	F␈↓↓␈α∧␈αy␈αε␈α␈↓	F␈↓↓␈α⊃␈αg(x,y)␈αε␈α␈↓	F␈↓↓))␈α⊃␈αP␈α⊂
␈↓ α∧␈↓↓␈↓	F␈↓↓)␈↓,

␈↓ α∧␈↓but␈α
then␈αwe␈α
will␈αstill␈α
use␈αthe␈α
comprehension␈αschema␈α
to␈αform␈α
the␈αset␈α
to␈αbe␈α
substituted␈αfor␈α
the␈αset
␈↓ α∧␈↓variable ␈↓	F␈↓.

␈↓ α∧␈↓␈↓ αTThe␈α
axiom␈α
schema␈α
of␈α
induction␈α
in␈α
arithmetic␈α
is␈α
the␈α
result␈α
of␈α
applying␈α
circumscription␈α
to␈α
the
␈↓ α∧␈↓constant 0 and the successor operation.

␈↓ α∧␈↓␈↓ αTThere␈α∞is␈α
a␈α∞way␈α
of␈α∞applying␈α
circumscription␈α∞to␈α
an␈α∞arbitrary␈α
sentence␈α∞of␈α∞predicate␈α
calculus.
␈↓ α∧␈↓Let␈α␈↓↓p␈↓␈αbe␈αsuch␈αa␈αsentence␈αand␈αlet␈α␈↓	F␈↓␈αbe␈αa␈αpredicate␈αsymbol.␈α The␈α␈↓↓relativization␈↓␈αof␈α␈↓↓p␈↓␈αwith␈αrespect␈αto
␈↓ α∧␈↓␈↓	F␈↓␈α(written␈α␈↓↓p␈↓	␈↓#
F␈↓#␈↓)␈αis␈αdefined␈α(as␈αin␈αsome␈αlogic␈αtexts)␈αas␈αthe␈αsentence␈αthat␈αresults␈αfrom␈αreplacing␈αevery
␈↓ α∧␈↓quantification␈α␈↓↓(∀x)E␈↓␈αthat␈αoccurs␈αin␈α␈↓↓p␈↓␈αby␈α␈↓↓(∀x)(␈↓	F␈↓↓(x) ⊃ E)␈↓␈αand␈αevery␈αquantification␈α␈↓↓(∃x)E␈↓␈αthat␈αoccurs
␈↓ α∧␈↓in ␈↓↓p␈↓ by ␈↓↓(∃x)(␈↓	F␈↓↓(x) ∧ E)␈↓.  The circumscription of ␈↓↓p␈↓ is then the sentence

␈↓ α∧␈↓4)␈↓ αt ␈↓↓p␈↓	␈↓#
F␈↓#␈↓↓ ⊃ (∀x)(P(x) ⊃ ␈↓	F␈↓↓(x))␈↓.

␈↓ α∧␈↓This␈α∞form␈α
is␈α∞correct␈α
only␈α∞if␈α
neither␈α∞constants␈α
nor␈α∞function␈α
symbols␈α∞occur␈α
in␈α∞␈↓↓p.␈↓␈α
If␈α∞they␈α
do,␈α∞it␈α
is
␈↓ α∧␈↓necessary␈α∂to␈α∂conjoin␈α∂␈↓↓␈↓	F␈↓↓(c)␈↓␈α⊂for␈α∂each␈α∂constant␈α∂␈↓↓c␈↓␈α⊂and␈α∂␈↓↓(∀x)(␈↓	F␈↓↓(x) ⊃ ␈↓	F␈↓↓(f(x)))␈↓␈α∂for␈α∂each␈α⊂single␈α∂argument
␈↓ α∧␈↓function␈αsymbol␈α
␈↓↓f␈↓␈αto␈α
the␈αpremiss␈αof␈α
(4).␈α Corresponding␈α
sentences␈αmust␈αbe␈α
conjoined␈αif␈α
there␈αare
␈↓ α∧␈↓function␈αsymbols␈αof␈αtwo␈αor␈αmore␈αarguments.␈α The␈αintuitive␈αmeaning␈αof␈α(4)␈αis␈αthat␈αthe␈αonly␈αobjects
␈↓ α∧␈↓satisfying ␈↓↓P␈↓ that exist are those that the sentence ␈↓↓p␈↓ forces to exist.

␈↓ α∧␈↓␈↓ αTApplying␈α∂the␈α∞circumscription␈α∂schema␈α∞requires␈α∂inventing␈α∞a␈α∂suitable␈α∞predicate␈α∂to␈α∞substitute
␈↓ α∧␈↓for␈α
the␈α
symbol␈α
␈↓	F␈↓␈α∞(inventing␈α
a␈α
suitable␈α
set␈α
in␈α∞the␈α
set-theoretic␈α
formulation).␈α
 In␈α
this␈α∞it␈α
resembles
␈↓ α∧␈↓mathematical␈αinduction;␈αin␈αorder␈αto␈αget␈αthe␈αconclusion,␈αwe␈αmust␈αinvent␈αa␈αpredicate␈αfor␈α
which␈αthe
␈↓ α∧␈↓premiss is true.

␈↓ α∧␈↓␈↓ αTThere␈α∞is␈α∞also␈α∞a␈α∞semantic␈α∞way␈α∞of␈α∞looking␈α∞at␈α∞applying␈α∞circumscription.␈α∞ Namely,␈α∂a␈α∞sentence
␈↓ α∧␈↓that␈α∂can␈α∂be␈α∂proved␈α∂from␈α∂a␈α∂sentence␈α∂␈↓↓p␈↓␈α∞by␈α∂circumscription␈α∂is␈α∂true␈α∂in␈α∂all␈α∂minimal␈α∂models␈α∂of␈α∞␈↓↓p,␈↓
␈↓ α∧␈↓where␈α∂a␈α∂deduction␈α∂from␈α∞␈↓↓p␈↓␈α∂is␈α∂true␈α∂in␈α∂all␈α∞models␈α∂of␈α∂␈↓↓p.␈↓␈α∂Minimality␈α∞is␈α∂defined␈α∂with␈α∂respect␈α∂to␈α∞a
␈↓ α∧␈↓containment␈α⊂relation␈α⊂≤.␈α⊂ We␈α⊂write␈α∂that␈α⊂␈↓↓M1 ≤ M2␈↓␈α⊂if␈α⊂every␈α⊂element␈α∂of␈α⊂the␈α⊂domain␈α⊂of␈α⊂␈↓↓M1␈↓␈α⊂is␈α∂a
␈↓ α∧␈↓member␈α
of␈α
the␈α
domain␈α
of␈α∞␈↓↓M2␈↓␈α
and␈α
on␈α
the␈α
common␈α∞members␈α
all␈α
predicates␈α
have␈α
the␈α∞same␈α
truth
␈↓ α∧␈↓␈↓ u8


␈↓ α∧␈↓value.␈α∩ It␈α∩is␈α∩not␈α∩always␈α∪true␈α∩that␈α∩a␈α∩sentence␈α∩true␈α∩in␈α∪all␈α∩minimal␈α∩models␈α∩can␈α∩be␈α∪proved␈α∩by
␈↓ α∧␈↓circumscription.␈α
 Indeed␈α
the␈α
minimal␈α
model␈α
of␈α
Peano's␈α
axioms␈α
is␈α
the␈α
standard␈α
model␈α
of␈α
arithmetic,
␈↓ α∧␈↓and␈α∂G:␈↓↓odel's␈α∂theorem␈α∂is␈α∂the␈α∂assertion␈α∂that␈α∞not␈α∂all␈α∂true␈α∂sentences␈α∂are␈α∂theorems.␈α∂ Minimal␈α∞models
␈↓ α∧␈↓↓don't always exist, and when they exist, they aren't always unique.

␈↓ α∧␈↓␈↓ αT(McCarthy 1977a) treats circumscription in more detail.



␈↓ α∧␈↓␈↓αConcepts as objects␈↓

␈↓ α∧␈↓␈↓ αTWe␈αshall␈α
begin␈αby␈αdiscussing␈α
how␈αto␈αexpress␈α
such␈αfacts␈α
as␈α␈↓↓"Pat␈αknows␈α
the␈αcombination␈αof␈α
the
␈↓ α∧␈↓↓safe"␈↓,␈αalthough␈αthe␈α
idea␈αof␈αtreating␈αa␈α
concept␈αas␈αan␈αobject␈α
has␈αapplication␈αbeyond␈α
the␈αdiscussion
␈↓ α∧␈↓of knowledge.

␈↓ α∧␈↓␈↓ αTWe␈α⊃shall␈α⊃use␈α⊃the␈α⊃symbol␈α⊃␈↓↓safe1␈↓␈α⊃for␈α⊂the␈α⊃safe,␈α⊃and␈α⊃␈↓↓combination(s)␈↓␈α⊃is␈α⊃our␈α⊃notation␈α⊃for␈α⊂the
␈↓ α∧␈↓combination␈α∞of␈α∞an␈α∞arbitrary␈α∞safe␈α∞␈↓↓s␈↓.␈α∞ We␈α∞aren't␈α∞much␈α∞interested␈α∞in␈α∞the␈α∞domain␈α∞of␈α
combinations,
␈↓ α∧␈↓and␈α⊃we␈α∩shall␈α⊃take␈α⊃them␈α∩to␈α⊃be␈α⊃strings␈α∩of␈α⊃digits␈α⊃with␈α∩dashes␈α⊃in␈α⊃the␈α∩right␈α⊃place,␈α⊃and,␈α∩since␈α⊃a
␈↓ α∧␈↓combination is a string, we will write it in quotes.  Thus we can write

␈↓ α∧␈↓5)␈↓ αt ␈↓↓combination(safe1) = "45-25-17"␈↓

␈↓ α∧␈↓as␈αa␈αformalization␈αof␈αthe␈αEnglish␈α␈↓↓"The␈αcombination␈αof␈αthe␈αsafe␈αis␈α45-25-17"␈↓.␈α Let␈αus␈αsuppose␈αthat
␈↓ α∧␈↓the combination of ␈↓↓safe2␈↓ is, co-incidentally, also 45-25-17, so we can also write

␈↓ α∧␈↓6)␈↓ αt ␈↓↓combination(safe2) = "45-25-17"␈↓.

␈↓ α∧␈↓␈↓ αTNow␈αwe␈αwant␈αto␈αtranslate␈α␈↓↓"Pat␈αknows␈αthe␈αcombination␈αof␈αthe␈αsafe"␈↓.␈α If␈αwe␈αwere␈αto␈αexpress␈αit
␈↓ α∧␈↓as

␈↓ α∧␈↓7)␈↓ αt *␈↓↓knows(pat,combination(safe1))␈↓,

␈↓ α∧␈↓the␈αinference␈αrule␈αthat␈α
allows␈αreplacing␈αa␈αterm␈α
by␈αan␈αequal␈αterm␈αin␈α
first␈αorder␈αlogic␈αwould␈α
let␈αus
␈↓ α∧␈↓conclude

␈↓ α∧␈↓8)␈↓ αt *␈↓↓knows(pat,combination(safe2))␈↓,

␈↓ α∧␈↓which mightn't be true.

␈↓ α∧␈↓␈↓ αTThis␈α∞problem␈α∞was␈α∞already␈α
recognized␈α∞in␈α∞1879␈α∞by␈α
Frege,␈α∞the␈α∞founder␈α∞of␈α∞modern␈α
predicate
␈↓ α∧␈↓logic,␈α∀who␈α∀distinguished␈α∀between␈α∀direct␈α∃and␈α∀indirect␈α∀occurrences␈α∀of␈α∀expressions␈α∃and␈α∀would
␈↓ α∧␈↓consider␈α
the␈αoccurrence␈α
of␈α␈↓↓combination(safe1)␈↓␈α
in␈α(7)␈α
to␈αbe␈α
indirect␈αand␈α
not␈αsubject␈α
to␈αreplacement
␈↓ α∧␈↓of␈αequals␈αby␈αequals.␈α The␈αmodern␈αway␈αof␈α
stating␈αthe␈αproblem␈αis␈αto␈αcall␈α␈↓↓Pat␈αknows␈↓␈α
a␈αreferentially
␈↓ α∧␈↓opaque operator.

␈↓ α∧␈↓␈↓ αTThe␈α⊂way␈α∂out␈α⊂of␈α⊂this␈α∂difficulty␈α⊂currently␈α⊂most␈α∂popular␈α⊂is␈α∂to␈α⊂treat␈α⊂␈↓↓Pat␈α∂knows␈↓␈α⊂as␈α⊂a␈α∂␈↓↓modal
␈↓ α∧␈↓↓operator␈↓.␈α⊂ This␈α⊂involves␈α∂changing␈α⊂the␈α⊂logic␈α⊂so␈α∂that␈α⊂replacement␈α⊂of␈α∂an␈α⊂expression␈α⊂by␈α⊂an␈α∂equal
␈↓ α∧␈↓expression␈α∂is␈α∞not␈α∂allowed␈α∂in␈α∞opaque␈α∂contexts.␈α∂ Knowledge␈α∞is␈α∂not␈α∂the␈α∞only␈α∂operator␈α∂that␈α∞admits
␈↓ α∧␈↓modal␈α
treatment.␈α
 There␈αis␈α
also␈α
belief,␈αwanting,␈α
and␈α
logical␈α
or␈αphysical␈α
necessity.␈α
 For␈αAI␈α
purposes,
␈↓ α∧␈↓␈↓ u9


␈↓ α∧␈↓we␈α
would␈α
need␈α∞all␈α
the␈α
above␈α∞modal␈α
operators␈α
and␈α∞many␈α
more␈α
in␈α∞the␈α
same␈α
system.␈α∞ This␈α
would
␈↓ α∧␈↓make␈α
the␈α
semantic␈α
discussion␈αof␈α
the␈α
resulting␈α
modal␈α
logic␈αextremely␈α
complex.␈α
 For␈α
this␈αreason,␈α
and
␈↓ α∧␈↓because␈α
we␈αwant␈α
functions␈α
from␈αmaterial␈α
objects␈α
to␈αconcepts␈α
of␈α
them,␈αwe␈α
have␈α
followed␈αa␈α
different
␈↓ α∧␈↓path␈α⊂-␈α⊂introducing␈α⊂concepts␈α⊂as␈α⊂individual␈α∂objects.␈α⊂ This␈α⊂has␈α⊂not␈α⊂been␈α⊂popular␈α⊂in␈α∂philosophy,
␈↓ α∧␈↓although I suppose no-one would doubt that it could be done.

␈↓ α∧␈↓␈↓ αTOur␈αapproach␈αis␈αto␈αintroduce␈αthe␈αsymbol␈α␈↓↓Safe1␈↓␈αas␈αa␈αname␈αfor␈αthe␈αconcept␈αof␈αsafe1␈αand␈αthe
␈↓ α∧␈↓function␈α∂␈↓↓Combination␈↓␈α⊂which␈α∂takes␈α⊂a␈α∂concept␈α⊂of␈α∂a␈α⊂safe␈α∂into␈α⊂a␈α∂concept␈α⊂of␈α∂its␈α⊂combination.␈α∂ The
␈↓ α∧␈↓second operand of the function ␈↓↓knows␈↓ is now required to be a concept, and we can write

␈↓ α∧␈↓9)␈↓ αt ␈↓↓knows(pat,Combination(Safe1))␈↓

␈↓ α∧␈↓to␈αassert␈αthat␈αPat␈αknows␈α
the␈αcombination␈αof␈αsafe1.␈α The␈αprevious␈α
trouble␈αis␈αavoided␈αso␈αlong␈αas␈α
we
␈↓ α∧␈↓can assert

␈↓ α∧␈↓10)␈↓ αt ␈↓↓Combination(Safe1) ≠ Combination(Safe2)␈↓,

␈↓ α∧␈↓which␈αis␈αquite␈αreasonable,␈αsince␈αwe␈αdo␈αnot␈αconsider␈αthe␈αconcept␈αof␈αthe␈αcombination␈αof␈α␈↓↓safe1␈↓␈αto␈αbe
␈↓ α∧␈↓the␈αsame␈αas␈αthe␈αconcept␈αof␈αthe␈αcombination␈αof␈α␈↓↓safe2␈↓,␈αeven␈αif␈αthe␈αcombinations␈αthemselves␈αare␈αthe
␈↓ α∧␈↓same.

␈↓ α∧␈↓␈↓ αTWe write

␈↓ α∧␈↓11)␈↓ αt ␈↓↓denotes(Safe1,safe1)␈↓

␈↓ α∧␈↓and say that ␈↓↓safe1␈↓ is the denotation of ␈↓↓Safe1␈↓.  We can say that Pegasus doesn't exist by writing

␈↓ α∧␈↓12)␈↓ αt ␈↓↓¬(∃x)(denotes(Pegasus,x))␈↓

␈↓ α∧␈↓still␈α
admitting␈α
␈↓↓Pegasus␈↓␈α
as␈α
a␈α
perfectly␈α
good␈αconcept.␈α
 If␈α
we␈α
only␈α
admit␈α
concepts␈α
with␈αdenotations␈α
(or
␈↓ α∧␈↓admit␈αpartial␈αfunctions␈αinto␈αour␈αsystem),␈αwe␈αcan␈αregard␈αdenotation␈αas␈αa␈αfunction␈αfrom␈αconcepts␈αto
␈↓ α∧␈↓objects - including other concepts.  We can then write

␈↓ α∧␈↓13)␈↓ αt ␈↓↓safe1 = den(Safe1)␈↓.

␈↓ α∧␈↓␈↓ αTThe␈α⊗functions␈α∃␈↓↓combination␈↓␈α⊗and␈α∃␈↓↓Combination␈↓␈α⊗are␈α∃related␈α⊗in␈α∃a␈α⊗way␈α∃that␈α⊗we␈α⊗may␈α∃call
␈↓ α∧␈↓extensional, namely

␈↓ α∧␈↓14)␈↓ αt ␈↓↓(∀S)(combination(den(S)) = den(Combination(S))␈↓,

␈↓ α∧␈↓and we can also write this relation in terms of ␈↓↓Combination␈↓ alone as

␈↓ α∧␈↓15)␈↓ αt ␈↓↓(∀S1 S2)(den(S1) = den(S2) ⊃ den(Combination(S1)) = den(Combination(S2)))␈↓,

␈↓ α∧␈↓or, in terms of the denotation predicate,

␈↓ α∧␈↓16)␈↓ αt␈α!␈↓↓(∀S1␈α"S2␈α!s␈α"c)(denotes(S1,s)␈α!∧␈α"denotes(S2,s)␈α!∧␈α"denotes(Combination(S1),c)␈α!⊃
␈↓ α∧␈↓↓denotes(Combination(S2),c))␈↓.
␈↓ α∧␈↓␈↓ f10


␈↓ α∧␈↓It␈α
is␈αprecisely␈α
this␈αproperty␈α
of␈αextensionality␈α
that␈α
the␈αabove-mentioned␈α
␈↓↓knows␈↓␈αpredicate␈α
lacks␈αin␈α
its
␈↓ α∧␈↓second argument; it is extensional in its first argument.

␈↓ α∧␈↓␈↓ αTSuppose␈α∞we␈α∞now␈α
want␈α∞to␈α∞say␈α
␈↓↓"Pat␈α∞knows␈α∞that␈α
Mike␈α∞knows␈α∞the␈α
combination␈α∞of␈α∞safe1"␈↓.␈α
 We
␈↓ α∧␈↓cannot␈α⊃use␈α⊂␈↓↓knows(mike,Combination(Safe1))␈↓␈α⊃as␈α⊃an␈α⊂operand␈α⊃of␈α⊃another␈α⊂␈↓↓knows␈↓␈α⊃function␈α⊃for␈α⊂two
␈↓ α∧␈↓reasons.␈α First,␈αthe␈αvalue␈αof␈α␈↓↓knows(person,Concept)␈↓␈αis␈αa␈αtruth␈αvalue,␈αand␈αthere␈αare␈αonly␈α
two␈αtruth
␈↓ α∧␈↓values,␈αso␈αwe␈αwould␈αeither␈αhave␈αPat␈α
knowing␈αall␈αtrue␈αstatements␈αor␈αnone.␈α Second,␈α
English␈αtreats
␈↓ α∧␈↓knowledge␈α
of␈α
propositions␈αdifferently␈α
from␈α
the␈αway␈α
it␈α
treats␈αknowledge␈α
of␈α
the␈αvalue␈α
of␈α
a␈αterm.␈α
 To
␈↓ α∧␈↓know␈α
a␈α
proposition␈αis␈α
to␈α
know␈αthat␈α
it␈α
is␈α
true,␈αwhereas␈α
the␈α
analog␈αof␈α
knowing␈α
a␈αcombination␈α
would
␈↓ α∧␈↓be knowing whether the proposition is true.

␈↓ α∧␈↓␈↓ αTWe␈α)solve␈α(the␈α)first␈α)problem␈α(by␈α)introducing␈α(a␈α)new␈α)knowledge␈α(function
␈↓ α∧␈↓␈↓↓Knows(Personconcept,Concept)␈↓.␈α∃ ␈↓↓Knows(Mike,Combination(Safe1))␈↓␈α∃is␈α∃not␈α∃a␈α∃truth␈α∃value␈α∃but␈α∀a
␈↓ α∧␈↓␈↓↓proposition␈↓,␈α≤and␈α≤there␈α≥can␈α≤be␈α≤distinct␈α≤true␈α≥propositions.␈α≤ We␈α≤now␈α≤need␈α≥a␈α≤predicate
␈↓ α∧␈↓␈↓↓true(proposition)␈↓, so we can assert

␈↓ α∧␈↓17)␈↓ αt ␈↓↓true(Knows(Mike,Combination(Safe1))␈↓

␈↓ α∧␈↓which is equivalent to our old-style assertion

␈↓ α∧␈↓18)␈↓ αt ␈↓↓knows(mike,Combination(Safe1))␈↓.

␈↓ α∧␈↓We now write

␈↓ α∧␈↓19)␈↓ αt ␈↓↓true(Knows(Pat,Knows(Mike,Combination(Safe1))))␈↓

␈↓ α∧␈↓to assert that Pat knows ␈↓↓whether␈↓ Mike knows the combination of safe1.  We define

␈↓ α∧␈↓20)␈↓ αt␈α=␈↓↓(∀␈α>Person,Proposition)(K(Person,Proposition)␈α==␈α>true(Proposition)␈α=and
␈↓ α∧␈↓↓Knows(Person,Proposition))␈↓,

␈↓ α∧␈↓which␈αforms␈αthe␈αproposition␈α␈↓↓that␈↓␈αa␈αperson␈αknows␈αa␈αproposition␈αfrom␈αthe␈αtruth␈αof␈αthe␈αproposition
␈↓ α∧␈↓and␈α∪that␈α∪he␈α∪knows␈α∀whether␈α∪the␈α∪proposition␈α∪holds.␈α∪ Note␈α∀that␈α∪it␈α∪is␈α∪necessary␈α∪to␈α∀have␈α∪new
␈↓ α∧␈↓connectives␈αto␈αcombine␈αpropositions␈αand␈αthat␈αan␈αequality␈αsign␈αrather␈αthan␈αan␈αequivalence␈αsign␈αis
␈↓ α∧␈↓used.␈α As␈αfar␈α
as␈αour␈αfirst␈α
order␈αlogic␈αis␈α
concerned,␈α(20)␈αis␈α
an␈αassertion␈αof␈α
the␈αequality␈αof␈αtwo␈α
terms.
␈↓ α∧␈↓These matters are discussed thoroughly in (McCarthy 1977b).

␈↓ α∧␈↓␈↓ αTWhile␈α⊃a␈α⊂concept␈α⊃denotes␈α⊃at␈α⊂most␈α⊃one␈α⊂object,␈α⊃the␈α⊃same␈α⊂object␈α⊃can␈α⊂be␈α⊃denoted␈α⊃by␈α⊂many
␈↓ α∧␈↓concepts.␈α Nevertheless,␈αthere␈αare␈α
often␈αuseful␈αfunctions␈αfrom␈α
objects␈αto␈αconcepts␈αthat␈αdenote␈α
them.
␈↓ α∧␈↓Numbers␈αmay␈αconveniently␈αbe␈αregarded␈αhas␈αhaving␈α␈↓↓standard␈αconcepts␈↓,␈αand␈αan␈αobject␈αmay␈αhave␈αa
␈↓ α∧␈↓distinguished␈α⊂concept␈α⊃relative␈α⊂to␈α⊂a␈α⊃particular␈α⊂person.␈α⊂ (McCarthy␈α⊃1977b)␈α⊂illustrates␈α⊂the␈α⊃use␈α⊂of
␈↓ α∧␈↓functions␈αfrom␈αobjects␈αto␈αconcepts␈αin␈αformalizing␈αsuch␈αchestnuts␈αas␈αRussell's,␈α␈↓↓"I␈αthought␈αyour␈αyacht
␈↓ α∧␈↓↓was longer than it is"␈↓.

␈↓ α∧␈↓␈↓ αTThe␈αmost␈αimmediate␈αAI␈αproblem␈αthat␈αrequires␈αconcepts␈αfor␈αits␈αsuccessful␈αformalism␈αmay␈αbe
␈↓ α∧␈↓the␈α
relation␈αbetween␈α
knowledge␈α
and␈αability.␈α
 We␈α
would␈αlike␈α
to␈α
connect␈αMike's␈α
ability␈α
to␈αopen␈α
safe1
␈↓ α∧␈↓with␈α⊂his␈α⊃knowledge␈α⊂of␈α⊂the␈α⊃combination.␈α⊂ The␈α⊂proper␈α⊃formalization␈α⊂of␈α⊂the␈α⊃notion␈α⊂of␈α⊃␈↓↓can␈↓␈α⊂that
␈↓ α∧␈↓involves␈α⊃knowledge␈α⊃rather␈α∩than␈α⊃just␈α⊃physical␈α⊃possibility␈α∩hasn't␈α⊃been␈α⊃done␈α⊃yet.␈α∩ Moore␈α⊃(1977)
␈↓ α∧␈↓discusses␈α
the␈α
relation␈α
between␈α
knowledge␈α
and␈α
action␈αfrom␈α
a␈α
similar␈α
point␈α
of␈α
view,␈α
and␈α
the␈αfinal
␈↓ α∧␈↓version of (McCarthy 1977b) will contain some ideas about this.
␈↓ α∧␈↓␈↓ f11


␈↓ α∧␈↓␈↓ αTThere␈αare␈αobviously␈αsome␈αesthetic␈αdisadvantages␈αto␈αa␈αtheory␈αthat␈αhas␈αboth␈α␈↓↓mike␈↓␈αand␈α␈↓↓Mike␈↓.
␈↓ α∧␈↓Moreover,␈α∪natural␈α∪language␈α∪doesn't␈α∪make␈α∀such␈α∪distinctions␈α∪in␈α∪its␈α∪vocabulary,␈α∪but␈α∀in␈α∪rather
␈↓ α∧␈↓roundabout␈α
ways␈αwhen␈α
necessary.␈α
 Perhaps␈αwe␈α
could␈αmanage␈α
with␈α
just␈α␈↓↓Mike␈↓␈α
(the␈α
concept),␈αsince
␈↓ α∧␈↓the␈α␈↓↓denotation␈↓␈αfunction␈α
will␈αbe␈αavailable␈α
for␈αreferring␈αto␈α
␈↓↓mike␈↓␈α(the␈αperson␈α
himself).␈α It␈αmakes␈α
some
␈↓ α∧␈↓sentences␈αlonger,␈αand␈αwe␈αhave␈αto␈αuse␈αand␈αequivalence␈αrelation␈αwhich␈αwe␈αmay␈αcall␈α␈↓↓e␈↓αd␈↓↓enot␈↓␈α
and␈αsay
␈↓ α∧␈↓␈↓↓"Mike e␈↓αd␈↓↓enot Brother(Mary)"␈↓␈α
rather␈α
than␈α∞write␈α
␈↓↓"mike = brother(mary)"␈↓,␈α
reserving␈α
the␈α∞equality␈α
sign
␈↓ α∧␈↓for␈α
equal␈α
concepts.␈α
 Since␈α
many␈α
AI␈α
programs␈α
don't␈α
make␈α
much␈α
use␈α
of␈α
replacement␈α
of␈α
equals␈α
by
␈↓ α∧␈↓equals,␈α⊃their␈α⊂notation␈α⊃may␈α⊃admit␈α⊂either␈α⊃interpretation,␈α⊂i.e.,␈α⊃the␈α⊃formulas␈α⊂may␈α⊃stand␈α⊃for␈α⊂either
␈↓ α∧␈↓objects␈α
or␈αconcepts.␈α
 The␈α
biggest␈αobjection␈α
is␈α
that␈αthe␈α
semantics␈α
of␈αreasoning␈α
about␈α
objects␈αis␈α
more
␈↓ α∧␈↓complicated if one refers to them only via concepts.

␈↓ α∧␈↓␈↓ αTI␈α∩believe␈α⊃that␈α∩circumscription␈α∩will␈α⊃turn␈α∩out␈α⊃to␈α∩be␈α∩the␈α⊃key␈α∩to␈α∩inferring␈α⊃non-knowledge.
␈↓ α∧␈↓Unfortunately,␈αan␈α
adequate␈αformalism␈αhas␈α
not␈αyet␈α
been␈αdeveloped,␈αso␈α
we␈αcan␈α
only␈αgive␈αsome␈α
ideas
␈↓ α∧␈↓of␈α
why␈α
establishing␈α
non-knowledge␈αis␈α
important␈α
for␈α
AI␈αand␈α
how␈α
circumscription␈α
can␈αcontribute␈α
to
␈↓ α∧␈↓it.

␈↓ α∧␈↓␈↓ αTIf␈α
the␈α
robot␈α
can␈α
reason␈α
that␈α
it␈α
cannot␈α
open␈α
safe1,␈α
because␈α
it␈α
doesn't␈α
know␈α
the␈α
combination,␈α
it
␈↓ α∧␈↓can␈α⊂decide␈α⊂that␈α⊂its␈α⊂next␈α⊂task␈α⊂is␈α⊂to␈α∂find␈α⊂the␈α⊂combination.␈α⊂ However,␈α⊂if␈α⊂it␈α⊂has␈α⊂merely␈α⊂failed␈α∂to
␈↓ α∧␈↓determine␈αthe␈αcombination␈αby␈αreasoning,␈αmore␈αthinking␈αmight␈αsolve␈αthe␈αproblem.␈α If␈αit␈αcan␈αsafely
␈↓ α∧␈↓conclude␈αthat␈αthe␈αcombination␈αcannot␈αbe␈αdetermined␈α
by␈αreasoning,␈αit␈αcan␈αlook␈αfor␈αthe␈α
information
␈↓ α∧␈↓externally.

␈↓ α∧␈↓␈↓ αTAs␈αanother␈α
example,␈αsuppose␈αsomeone␈α
asks␈αyou␈α
whether␈αthe␈αPresident␈α
is␈αstanding,␈αsitting␈α
or
␈↓ α∧␈↓lying␈α∞down␈α
at␈α∞the␈α
moment␈α∞you␈α
read␈α∞the␈α∞paper.␈α
 Normally␈α∞you␈α
will␈α∞answer␈α
that␈α∞you␈α∞don't␈α
know
␈↓ α∧␈↓and␈α∞will␈α
not␈α∞respond␈α∞to␈α
a␈α∞suggestion␈α∞that␈α
you␈α∞think␈α
harder.␈α∞ You␈α∞conclude␈α
that␈α∞no␈α∞matter␈α
how
␈↓ α∧␈↓hard␈αyou␈αthink,␈αthe␈αinformation␈αisn't␈αto␈αbe␈αfound.␈α If␈αyou␈αreally␈αwant␈αto␈αknow,␈αyou␈αmust␈αlook␈αfor
␈↓ α∧␈↓an␈αexternal␈αsource␈αof␈αinformation.␈α
 How␈αdo␈αyou␈αknow␈αyou␈α
can't␈αsolve␈αthe␈αproblem?␈α The␈α
intuitive
␈↓ α∧␈↓answer␈αis␈αthat␈αany␈αanswer␈αis␈αconsistent␈αwith␈αyour␈αother␈αknowledge.␈α However,␈αyou␈αcertainly␈αdon't
␈↓ α∧␈↓construct␈α∀a␈α∀model␈α∀of␈α∀all␈α∀your␈α∀beliefs␈α∪to␈α∀establish␈α∀this.␈α∀ Since␈α∀you␈α∀undoubtedly␈α∀have␈α∪some
␈↓ α∧␈↓contradictory beliefs somewhere, you can't construct the required models anyway.

␈↓ α∧␈↓␈↓ αTThe␈α∂process␈α∂has␈α∞two␈α∂steps.␈α∂ The␈α∞first␈α∂is␈α∂deciding␈α∞what␈α∂knowledge␈α∂is␈α∞relevant.␈α∂ This␈α∂is␈α∞a
␈↓ α∧␈↓conjectural␈α
process,␈α
so␈α
its␈α
outcome␈αis␈α
not␈α
guaranteed␈α
to␈α
be␈α
correct.␈α It␈α
might␈α
be␈α
carried␈α
out␈αby␈α
some
␈↓ α∧␈↓kind of keyword retrieval from property lists, but there should be a less arbitrary method.

␈↓ α∧␈↓␈↓ αTThe␈α⊃second␈α⊃process␈α⊃uses␈α⊃the␈α⊃set␈α⊃of␈α⊃"relevant"␈α⊃sentences␈α⊃found␈α⊃by␈α⊃the␈α⊃first␈α⊃process␈α⊂and
␈↓ α∧␈↓constructs␈α⊂models␈α⊂or␈α⊂circumscription␈α⊃predicates␈α⊂that␈α⊂allow␈α⊂for␈α⊂both␈α⊃outcomes␈α⊂if␈α⊂what␈α⊂is␈α⊃to␈α⊂be
␈↓ α∧␈↓shown␈αunknown␈αis␈αa␈αproposition.␈α If␈αwhat␈αis␈αto␈αbe␈αshown␈αunknown␈αhas␈αmany␈αpossible␈αvalues␈αlike
␈↓ α∧␈↓a␈αsafe␈αcombination,␈αthen␈αsomething␈αmore␈αsophisticated␈αis␈αnecessary.␈α A␈αparameter␈αcalled␈αthe␈α
value
␈↓ α∧␈↓of␈α
the␈α
combination␈α∞is␈α
introduced,␈α
and␈α∞a␈α
"model"␈α
or␈α
circumscription␈α∞predicate␈α
is␈α
found␈α∞in␈α
which
␈↓ α∧␈↓this␈α
parameter␈αoccurs␈α
free.␈α
 We␈αused␈α
quotes,␈αbecause␈α
a␈α
one␈αparameter␈α
family␈αof␈α
models␈α
is␈αfound
␈↓ α∧␈↓rather than a single model.

␈↓ α∧␈↓␈↓ αTWe␈α
conclude␈αwith␈α
just␈α
one␈αexample␈α
of␈αa␈α
circumscription␈α
schema␈αdealing␈α
with␈αknowledge.␈α
 It
␈↓ α∧␈↓is formalization of the assertion that all Mike knows is a consequence of propositions ␈↓↓P␈↓ and ␈↓↓Q.␈↓

␈↓ α∧␈↓21)␈↓ αt ␈↓↓␈↓	F␈↓↓(P0) ∧ ␈↓	F␈↓↓(Q0) ∧ (∀P Q)(␈↓	F␈↓↓(P) ∧ ␈↓	F␈↓↓(P implies Q) ⊃ ␈↓	F␈↓↓(Q)) ⊃ (∀P)(knows(Mike,P) ⊃ ␈↓	F␈↓↓(P))␈↓.
␈↓ α∧␈↓␈↓ f12


␈↓ α∧␈↓␈↓αPhilosophical Notes␈↓

␈↓ α∧␈↓␈↓ αTPhilosophy␈αhas␈αa␈αmore␈αdirect␈αrelation␈α
to␈αartificial␈αintelligence␈αthan␈αit␈αhas␈αto␈α
other␈αsciences.
␈↓ α∧␈↓Both␈αsubjects␈αrequire␈αthe␈αformalization␈αof␈αcommon␈αsense␈αknowledge␈αand␈αrepair␈αof␈αits␈αdeficiencies.
␈↓ α∧␈↓Since␈αa␈α
robot␈αwith␈αgeneral␈α
intelligence␈αrequires␈α
some␈αgeneral␈αview␈α
of␈αthe␈α
world,␈αdeficiencies␈αin␈α
the
␈↓ α∧␈↓programmers'␈αintrospection␈α
of␈αtheir␈α
own␈αworld-views␈αcan␈α
result␈αin␈α
operational␈αweaknesses␈α
in␈αthe
␈↓ α∧␈↓program.␈α⊃ Thus␈α⊂many␈α⊃programs,␈α⊃including␈α⊂Winograd's␈α⊃SHRDLU,␈α⊃regard␈α⊂the␈α⊃history␈α⊃of␈α⊂their
␈↓ α∧␈↓world␈αas␈α
a␈αsequence␈αof␈α
situations␈αeach␈αof␈α
which␈αis␈αproduced␈α
by␈αan␈αevent␈α
occuring␈αin␈α
a␈αprevious
␈↓ α∧␈↓situation␈α
of␈α
the␈α
sequence.␈α
 To␈α
handle␈α
concurrent␈α
events,␈α
such␈α
programs␈α
must␈α
be␈α
rebuilt␈α
and␈αnot
␈↓ α∧␈↓just provided with more facts.

␈↓ α∧␈↓␈↓ αTThis␈α∂section␈α∂is␈α∂organized␈α∂as␈α∂a␈α⊂collection␈α∂of␈α∂disconnected␈α∂remarks␈α∂some␈α∂of␈α∂which␈α⊂have␈α∂a
␈↓ α∧␈↓direct␈α
technical␈α∞character,␈α
while␈α∞others␈α
concern␈α∞the␈α
general␈α∞structure␈α
of␈α∞knowledge␈α
of␈α∞the␈α
world.
␈↓ α∧␈↓Some␈α∩of␈α∩them␈α∩simply␈α⊃give␈α∩sophisticated␈α∩justifications␈α∩for␈α⊃some␈α∩things␈α∩that␈α∩programmers␈α⊃are
␈↓ α∧␈↓inclined to do anyway, so some people may regard them as superfluous.

␈↓ α∧␈↓␈↓ αT1.␈αBuilding␈αa␈αview␈α
of␈αthe␈αworld␈αinto␈α
the␈αstructure␈αof␈αa␈αprogram␈α
does␈αnot␈αin␈αitself␈α
give␈αthe
␈↓ α∧␈↓program␈α⊂the␈α∂ability␈α⊂to␈α∂state␈α⊂the␈α⊂view␈α∂explicitly.␈α⊂ Thus,␈α∂none␈α⊂of␈α∂the␈α⊂programs␈α⊂that␈α∂presuppose
␈↓ α∧␈↓history␈α∞as␈α∞a␈α∂sequence␈α∞of␈α∞situations␈α∞can␈α∂make␈α∞the␈α∞assertion␈α∞␈↓↓"History␈α∂is␈α∞a␈α∞sequence␈α∂of␈α∞situations"␈↓.
␈↓ α∧␈↓Indeed,␈α∃for␈α∀a␈α∃human␈α∀to␈α∃make␈α∀his␈α∃presuppositions␈α∀explicit␈α∃is␈α∀often␈α∃beyond␈α∃his␈α∀individual
␈↓ α∧␈↓capabilities,␈αand␈αthe␈αsciences␈αof␈αpsychology␈αand␈αphilosophy␈αstill␈αhave␈αunsolved␈αproblems␈αin␈αdoing
␈↓ α∧␈↓so.

␈↓ α∧␈↓␈↓ αT2.␈α
Common␈α
sense␈α
requires␈α
scientific␈α
formulation.␈α
 Both␈α
AI␈α
and␈α
philosophy␈α
require␈α∞it,␈α
and
␈↓ α∧␈↓philosophy might even be regarded as an attempt to make common sense into a science.

␈↓ α∧␈↓␈↓ αT3.␈α⊗AI␈α⊗and␈α⊗philosophy␈α∃both␈α⊗suffer␈α⊗from␈α⊗the␈α∃following␈α⊗dilemma.␈α⊗ Both␈α⊗need␈α∃precise
␈↓ α∧␈↓formalizations,␈α∪but␈α∪the␈α∪fundamental␈α∪structure␈α∪of␈α∩the␈α∪world␈α∪has␈α∪not␈α∪yet␈α∪been␈α∪discovered,␈α∩so
␈↓ α∧␈↓imprecise␈α∃and␈α⊗even␈α∃inconsistent␈α⊗formulations␈α∃need␈α∃to␈α⊗be␈α∃used.␈α⊗ If␈α∃the␈α⊗imprecision␈α∃merely
␈↓ α∧␈↓concerned␈α∞the␈α∞values␈α∞to␈α∞be␈α∞given␈α∂to␈α∞numerical␈α∞constants,␈α∞there␈α∞wouldn't␈α∞be␈α∞great␈α∂difficulty,␈α∞but
␈↓ α∧␈↓there␈αis␈αa␈αneed␈αto␈αuse␈αtheories␈αwhich␈αare␈αgrossly␈αwrong␈αin␈αgeneral␈αwithin␈αdomains␈αwhere␈αthey␈αare
␈↓ α∧␈↓valid.␈α The␈αabove-mentioned␈α␈↓↓history-as-a-sequence-of-situations␈↓␈αis␈αsuch␈αa␈αtheory.␈α The␈αsense␈αin
␈↓ α∧␈↓which this theory is an approximation to a more sophisticated theory hasn't been examined.

␈↓ α∧␈↓␈↓ αT4.␈α⊂(McCarthy␈α⊂1977c)␈α⊂discusses␈α⊂the␈α⊂need␈α⊃to␈α⊂use␈α⊂concepts␈α⊂that␈α⊂are␈α⊂meaningful␈α⊂only␈α⊃in␈α⊂an
␈↓ α∧␈↓approximate␈α∨theory.␈α∨ Relative␈α∨to␈α≡a␈α∨Cartesian␈α∨product␈α∨co-ordinatization␈α∨of␈α≡situations,
␈↓ α∧␈↓counterfactual␈α
sentences␈α
of␈α
the␈α
form␈α
␈↓↓"If␈α
co-ordinate␈αx␈α
had␈α
the␈α
value␈α
c␈α
and␈α
the␈α
other␈αco-ordinates
␈↓ α∧␈↓↓retained␈α
their␈α
values,␈α
then␈α
p␈α
would␈α
be␈α
true"␈↓␈α
can␈α
be␈α
meaningful.␈α
 Thus,␈α
within␈α
a␈α
suitable␈αtheory,
␈↓ α∧␈↓the␈α∂assertion␈α∂␈↓↓"The␈α∂skier␈α⊂wouldn't␈α∂have␈α∂fallen␈α∂if␈α⊂he␈α∂had␈α∂put␈α∂his␈α⊂weight␈α∂on␈α∂his␈α∂downhill␈α⊂ski"␈↓␈α∂is
␈↓ α∧␈↓meaningful␈αand␈αperhaps␈αtrue,␈αbut␈αit␈αis␈αhard␈αto␈αgive␈αit␈αmeaning␈αas␈αa␈αstatement␈αabout␈αthe␈αworld␈αof
␈↓ α∧␈↓atoms␈α
and␈αwave␈α
functions,␈αbecause␈α
it␈αis␈α
not␈αclear␈α
what␈αdifferent␈α
wave␈αfunctions␈α
are␈α
specified␈αby
␈↓ α∧␈↓␈↓↓"if␈α∂he␈α⊂had␈α∂put␈α∂his␈α⊂weight␈α∂on␈α∂his␈α⊂downhill␈α∂ski"␈↓.␈α∂ We␈α⊂need␈α∂an␈α∂AI␈α⊂formalism␈α∂that␈α∂can␈α⊂use␈α∂such
␈↓ α∧␈↓statements␈α∪but␈α∩can␈α∪go␈α∩beyond␈α∪them␈α∪to␈α∩the␈α∪next␈α∩level␈α∪of␈α∩approximation␈α∪when␈α∪possible␈α∩and
␈↓ α∧␈↓necessary.␈α
 I␈α
now␈α
think␈α
that␈αcircumscription␈α
is␈α
a␈α
tool␈α
that␈αwill␈α
allow␈α
drawing␈α
conclusions␈α
from␈αa
␈↓ α∧␈↓given␈α⊃approximate␈α∩theory␈α⊃for␈α⊃use␈α∩in␈α⊃given␈α∩circumstances␈α⊃without␈α⊃a␈α∩total␈α⊃commitment␈α∩to␈α⊃the
␈↓ α∧␈↓theory.

␈↓ α∧␈↓␈↓ αT5.␈αOne␈αcan␈αimagine␈αconstructing␈αprograms␈αeither␈αas␈αempiricists␈αor␈αas␈αrealists.␈α An␈α
empiricist
␈↓ α∧␈↓program␈α
would␈α
build␈α
only␈α
theories␈α
connecting␈α
its␈α
sense␈α
data␈α
with␈α
its␈α
actions.␈α
 A␈α∞realist␈α
program
␈↓ α∧␈↓␈↓ f13


␈↓ α∧␈↓would␈α
try␈α
to␈α
find␈α
facts␈αabout␈α
a␈α
world␈α
that␈α
existed␈αindependently␈α
of␈α
the␈α
program␈α
and␈α
would␈αnot
␈↓ α∧␈↓suppose that the only reality is what might somehow interact with the program.

␈↓ α∧␈↓␈↓ αTI␈αfavor␈α
building␈αrealist␈α
programs␈αwith␈α
the␈αfollowing␈αexample␈α
in␈αmind.␈α
 It␈αhas␈α
been␈αshown
␈↓ α∧␈↓that␈αthe␈αLife␈αtwo␈αdimensional␈αcellular␈αautomaton␈αis␈αuniversal␈αas␈αa␈αcomputer␈αand␈αas␈αa␈αconstructor.
␈↓ α∧␈↓Therefore,␈α∞there␈α
could␈α∞be␈α
configurations␈α∞of␈α
Life␈α∞cells␈α
acting␈α∞as␈α
self-reproducing␈α∞computers␈α
with
␈↓ α∧␈↓sensory␈αand␈αmotor␈αcapabilities␈αwith␈αrespect␈αto␈αthe␈αrest␈αof␈αthe␈αLife␈αplane.␈α The␈αprogram␈αin␈αsuch␈αa
␈↓ α∧␈↓computer␈α∞could␈α
study␈α∞the␈α
physics␈α∞of␈α
its␈α∞world␈α
by␈α∞making␈α
theories␈α∞and␈α
experiments␈α∞to␈α∞test␈α
them
␈↓ α∧␈↓and␈α∞might␈α∞eventually␈α∞come␈α∞up␈α∞with␈α∞the␈α∞theory␈α∞that␈α∞its␈α∞fundamental␈α∞physics␈α∞is␈α∞that␈α∞of␈α∞the␈α∞Life
␈↓ α∧␈↓cellular automaton.

␈↓ α∧␈↓␈↓ αTWe␈α∂can␈α∞test␈α∂our␈α∞theories␈α∂of␈α∂epistemology␈α∞and␈α∂common␈α∞sense␈α∂reasoning␈α∞by␈α∂asking␈α∂if␈α∞they
␈↓ α∧␈↓would␈α
permit␈α
the␈α
Life-world␈α
computer␈α
to␈α∞conclude,␈α
on␈α
the␈α
basis␈α
of␈α
experiments,␈α
that␈α∞its␈α
physics
␈↓ α∧␈↓was␈α
that␈α
of␈αLife.␈α
 If␈α
our␈αepistemology␈α
isn't␈α
adequate␈α
for␈αsuch␈α
a␈α
simple␈αuniverse,␈α
it␈α
surely␈αisn't␈α
good
␈↓ α∧␈↓enough␈α∪for␈α∩our␈α∪much␈α∪more␈α∩complicated␈α∪universe.␈α∪ This␈α∩example␈α∪is␈α∪one␈α∩of␈α∪the␈α∪reasons␈α∩for
␈↓ α∧␈↓preferring␈α∂to␈α⊂build␈α∂realist␈α∂rather␈α⊂than␈α∂empiricist␈α⊂programs.␈α∂ The␈α∂empiricist␈α⊂program,␈α∂if␈α⊂it␈α∂was
␈↓ α∧␈↓smart␈α
enough,␈α
would␈α
only␈α
end␈α
up␈α
with␈α
a␈α
statement␈α
that␈α
␈↓↓"my␈α
experiences␈α
are␈α
best␈α
organized␈α∞as␈α
if
␈↓ α∧␈↓↓there␈α∞were␈α∂a␈α∞Life␈α∂cellular␈α∞automaton␈α∞and␈α∂events␈α∞isomorphic␈α∂to␈α∞my␈α∞thoughts␈α∂occurred␈α∞in␈α∂a␈α∞certain
␈↓ α∧␈↓↓subconfiguration␈α
of␈α
it"␈↓.␈α
 Thus␈α
it␈α
would␈α
get␈α
a␈α
result␈α
equivalent␈α
to␈α
that␈α
of␈α
the␈α
realist␈α
program␈αbut
␈↓ α∧␈↓more complicated and with less certainty.

␈↓ α∧␈↓␈↓ αTMore␈αgenerally,␈αwe␈αcan␈α
imagine␈αa␈α␈↓↓metaphilosophy␈↓␈αthat␈α
has␈αthe␈αsame␈αrelation␈α
to␈αphilosophy
␈↓ α∧␈↓that␈α⊂metamathematics␈α⊃has␈α⊂to␈α⊃mathematics.␈α⊂ Metaphilosophy␈α⊃would␈α⊂study␈α⊃mathematical␈α⊂systems
␈↓ α∧␈↓consisting␈α⊂of␈α⊂an␈α∂"epistemologist"␈α⊂seeking␈α⊂knowledge␈α∂in␈α⊂accordance␈α⊂with␈α∂the␈α⊂epistemology␈α⊂to␈α∂be
␈↓ α∧␈↓tested␈αand␈α
interacting␈αwith␈αa␈α
"world".␈α It␈αwould␈α
study␈αwhat␈αinformation␈α
about␈αthe␈αworld␈α
a␈αgiven
␈↓ α∧␈↓philosophy␈α∪would␈α∪obtain.␈α∪ This␈α∪would␈α∪depend␈α∀also␈α∪on␈α∪the␈α∪structure␈α∪of␈α∪the␈α∪world␈α∀and␈α∪the
␈↓ α∧␈↓"epistemologist"'s opportunities to interact.

␈↓ α∧␈↓␈↓ αTAI␈α∩could␈α∩benefit␈α∩from␈α∩building␈α∩some␈α∪very␈α∩simple␈α∩systems␈α∩of␈α∩this␈α∩kind,␈α∩and␈α∪so␈α∩might
␈↓ α∧␈↓philosophy.



␈↓ α∧␈↓␈↓αReferences␈↓

␈↓ α∧␈↓␈↓αMcCarthy,␈α∪J.␈α∩and␈α∪Hayes,␈α∩P.J.␈↓␈α∪(1969)␈α∪Some␈α∩Philosophical␈α∪Problems␈α∩from␈α∪the␈α∪Standpoint␈α∩of
␈↓ α∧␈↓Artificial␈α∩Intelligence.␈α∪␈↓↓Machine␈α∩Intelligence␈α∩4␈↓,␈α∪pp.␈α∩463-502␈α∩(eds␈α∪Meltzer,␈α∩B.␈α∩and␈α∪Michie,␈α∩D.).
␈↓ α∧␈↓Edinburgh: Edinburgh University Press.

␈↓ α∧␈↓␈↓αMcCarthy,␈α∪J.␈↓␈α∩(1977a)␈α∪Minimal␈α∩Inference␈α∪-␈α∩A␈α∪New␈α∩Way␈α∪of␈α∩Jumping␈α∪to␈α∩Conclusions␈α∪(to␈α∩be
␈↓ α∧␈↓published).

␈↓ α∧␈↓␈↓αMcCarthy, J.␈↓ (1977b) First Order Theories of Individual Concepts (to be published).

␈↓ α∧␈↓␈↓αMcCarthy, J.␈↓ (1977c) Ascribing Mental Qualities to Machines (to be published).

␈↓ α∧␈↓␈↓αMoore, Robert C.␈↓ (1977) Reasoning about Knowledge and Action, ␈↓↓1977 IJCAI Proceedings␈↓.