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␈↓␈↓↓␈↓α␈↓α
␈↓ ↓H
Computer Science 226␈↓ ¬⊂   Representation Theory        Winter 1974
␈↓ ↓H
␈↓
␈↓ ↓H

␈↓ ↓H
␈↓ α_This␈α∞course␈α∞is␈α∞concerned␈α∞with␈α∞the␈α∞problem␈α∞of␈α∞representing␈α∞information␈α∞in␈α
the␈α
memory␈α
of␈α
a
␈↓ ↓Hcomputer␈αso␈αthat␈αprograms␈αcan␈αuse␈αthis␈αinformation␈αto␈α
behave␈α
intelligently.␈α
I␈α
have␈α
been␈α
pushing␈α
the
␈↓ ↓Himportance␈αof␈αthis␈αproblem␈αfor␈αfifteen␈αyears,␈αbut␈αnow␈αthere␈αis␈αgeneral␈αrecognition␈αthat␈αthis␈αis␈αa␈αkey
␈↓ ↓Hproblem␈α
for␈α
artificial␈α
intelligence.

␈↓ α_The␈α
information␈α
to␈α
be␈α
represented␈α
is␈α
what␈α
a␈α
program␈α
can␈α
know␈α
and␈αmust␈αknow␈αin␈αorder␈αto
␈↓ ↓Hsolve␈α
some␈α
class␈α
of␈α
problems␈α
of␈α
interest.␈α
The␈αmeaning␈αof␈αthe␈αphrase␈α␈↓↓must␈αknow␈↓␈αis␈αevident,␈αbut␈α␈↓↓can
␈↓ ↓Hknow␈↓␈α≠require␈α≠explanation.␈α≠First,␈α≠the␈α≠information␈α≠must␈α≠be␈α≠obtainable␈α~by␈α~observation,␈α~by
␈↓ ↓Hcommunication␈α∞or␈α∞by␈α
reasoning.␈α
Second,␈α
the␈α
information␈α
must␈α
be␈α
plausibly␈α
present.␈α
Thus␈α
it␈α
is␈α
not
␈↓ ↓Hplausible␈αthat␈αmost␈αpeople␈αhave␈αspecific␈αinformation␈αabout␈αhow␈αto␈αgo␈αfrom␈αFresno␈αto␈αMiami,␈αbut␈αit
␈↓ ↓His␈αplausible␈αthat␈αthey␈αhave␈αinformation␈αabout␈αtravel␈αwithin␈αthe␈αUnited␈αStates␈αadequate␈αto␈αsolve␈αthat
␈↓ ↓Hproblem.␈α
Third,␈α
the␈α
information␈α
must␈α
be␈α
present␈α
in␈α
a␈α
form␈α
adequate␈α
to␈α
solve␈α
the␈α
problems.

␈↓ α_The␈α∪importance␈α∪of␈α∪representation␈α∪problems␈α∪stems␈α∪from␈α∪the␈α∪fact␈α∪that␈α∪inadequacy␈α∪of␈α∪the
␈↓ ↓Hrepresentations␈α∃used␈α∃is␈α∃the␈α∃main␈α∀reason␈α∀for␈α∀the␈α∀limitations␈α∀of␈α∀present␈α∀programs␈α∀in␈α∀artificial
␈↓ ↓Hintelligence.

␈↓ ↓H␈↓αSome␈α
illustrations␈α
of␈α
the␈α
above␈α
contention␈↓

␈↓ α_While␈α∞the␈α
importance␈α
of␈α
the␈α
representation␈α
problem␈α
now␈α
has␈α
wide␈α
agreement␈α
among␈α
people
␈↓ ↓Hworking␈α
in␈α
AI,␈α
there␈α
is␈α
much␈α
confusion␈αand␈αlittle␈αagreement␈αon␈αwhat␈αis␈αthe␈αbest␈αapproach␈αtowards
␈↓ ↓Hsolving␈αit.␈αIn␈αparticular,␈αthere␈α
is␈α
the␈α
controversy␈α
over␈α
whether␈α
declarative␈α
representations,␈α
procedural
␈↓ ↓Hrepresentations,␈α"analogical␈αrepresentations"␈αor␈αstill␈αothers␈αare␈αbest.␈αThis␈αcourse␈αwill␈αtake␈αdeclarative
␈↓ ↓Hrepresentations␈α∩as␈α∩primary,␈α⊃but␈α⊃other␈α⊃schools␈α⊃of␈α⊃thought␈α⊃will␈α⊃be␈α⊃represented␈α⊃by␈α⊃guest␈α⊃lecturers.
␈↓ ↓HWithin␈α∞the␈α∞declarative␈α∞school,␈α∞there␈α
is␈α
further␈α
controversy␈α
over␈α
whether␈α
a␈α
system␈α
of␈α
mathematical
␈↓ ↓Hlogic␈α∂is␈α∂the␈α∂right␈α∂way␈α∂to␈α∂proceed␈α∂or␈α∂whether␈α∂something␈α∂based␈α∂on␈α∂ordinary␈α∂language␈α∞might␈α∞work
␈↓ ↓Hbetter.␈αThis␈αcourse␈αwill␈αmainly␈αexplore␈αthe␈αpossibilities␈αof␈αmathematical␈αlogic,␈αbut␈αwe␈αwill␈αhear␈αfrom
␈↓ ↓Hthe␈α
others␈α
too.

␈↓ α_The␈α
formalisms␈α
of␈α
mathematical␈α
logic␈α
require␈αpractice␈αfor␈αtheir␈αeffective␈αuse␈αand␈αno-one␈αhas
␈↓ ↓Henough␈α∃practice.␈α∀Even␈α∀mathematical␈α∀logicians␈α∀do␈α∀very␈α∀little␈α∀of␈α∀their␈α∀work␈α∀within␈α∀the␈α∀logical
␈↓ ↓Hformalisms␈α-␈αmost␈αof␈αit␈αis␈αinformal␈αmathematics␈αproving␈αthings␈α␈↓↓about␈↓␈αthe␈αformal␈αsystems.␈αBecause␈αof
␈↓ ↓Hthis,␈α
the␈α
existing␈α
formalisms␈α
are␈α
not␈α
very␈α
convenient␈αand␈αrequire␈αimprovement␈αin␈αvarious␈αrespects.
␈↓ ↓HWhich␈α
respects␈α
are␈α
not␈α
entirely␈α
easy␈α
to␈α
determine␈α
without␈α
more␈α
practice␈α
in␈α
using␈α
them.

␈↓ α_A␈α∞good␈α∞part␈α∞of␈α∞the␈α∞work␈α∞in␈α∞the␈α∞course␈α∞will␈α∞consist␈α∞of␈α∞expressing␈α∞facts␈α∞involved␈α
in␈α
common
␈↓ ↓Hsense␈α
problems␈α
and␈α
their␈α
solution␈α
in␈α
first␈α
order␈α
logic␈α
with␈α
set␈α
theory␈α
and␈α
proving␈α
that␈αa␈αproposed
␈↓ ↓Hsolution␈α∞to␈α∞the␈α
problem␈α
really␈α
is␈α
one.␈α
For␈α
this␈α
purpose,␈α
we␈α
will␈α
use␈α
␈↓αFOL␈↓,␈α
a␈α
proof␈α
checker␈α
for␈α
an
␈↓ ↓Hexpanded␈α⊃first␈α⊃order␈α⊃logic␈α⊃written␈α⊃and␈α⊃being␈α⊃further␈α⊃developed␈α⊃by␈α⊃Richard␈α⊃Weyhrauch␈α⊃of␈α⊂the
␈↓ ↓HStanford␈α∂Artificial␈α∂Intelligence␈α∂Laboratory.␈α∞Computer␈α∞and␈α∞terminal␈α∞time␈α∞at␈α∞the␈α∞Lab␈α∞will␈α∞be␈α∞made
␈↓ ↓Havailable␈α
and␈α
there␈α
will␈α
be␈α
some␈α
terminals␈α
on␈α
campus.

␈↓ α_There␈α∞will␈α∞be␈α∞no␈α∞teaching␈α∞assistant␈α∞in␈α∞the␈α∞course,␈α∞but␈α∞my␈α∞secretary,␈α∞Mrs.␈α∞Kasee␈α∞Menke␈α
will
␈↓ ↓Hhave␈α
available␈α
handouts␈α
and␈α
other␈α
material␈α
concerning␈α
the␈α
course.

␈↓ α_Reading␈α
material␈α
includes␈α
the␈α
following:

␈↓ α_1.␈α
The␈α
␈↓αFOL␈↓␈α
manual␈α
which␈α
will␈α
be␈α
distributed.

␈↓ α_2.␈αThree␈αpapers,␈α␈↓↓Programs␈αwith␈αCommon␈αSense,␈α
Situations,␈α
Actions␈α
and␈α
Causal␈α
Laws,␈↓␈α
and␈α
␈↓↓Some
␈↓ ↓HPhilosophical␈α
Problems␈α
from␈α
the␈α
Standpoint␈α
of␈α
Artificial␈α
Intelligence␈↓␈αwhich␈αgive␈αthe␈αbasic␈αapproach
␈↓ ↓Hto␈α
the␈α
representation␈α
problem␈α
at␈α
five␈α
year␈α
intervals.␈α
These␈α
will␈α
also␈α
be␈α
distributed.

␈↓ α_3.␈α∂Papers␈α∂by␈α∂Erik␈α∂Sandewall,␈α∂Marvin␈α∂Minsky,␈α∂and␈α∂others␈α∂which␈α∂will␈α∂be␈α∂on␈α∂reserve␈α∂in␈α∂the
␈↓ ↓Hcomputer␈α
science␈α
library.

␈↓ α_4.␈α∩On␈α∩mathematical␈α∩logic,␈α∩the␈α∩following␈α∩books␈α∩are␈α∩recommended:␈α∩␈↓↓Mathematical␈α⊃logic␈α⊃and
␈↓ ↓Hformalized␈αtheories:␈αA␈αSurvey␈αof␈αBasic␈αConcepts␈αand␈αResults␈↓␈αby␈αRobert␈αRogers.␈αThis␈αcovers␈αthe␈αmain
␈↓ ↓Htopics␈α
on␈αa␈αrather␈αinformal␈αlevel␈αsince␈αit␈αis␈αwritten␈αfor␈αphilosophers.␈α␈↓↓Set␈αTheory␈αand␈αthe␈αContinuum
␈↓ ↓HHypothesis␈↓␈αchapters␈α1␈αand␈α2␈αby␈αPaul␈α
Cohen.␈α
This␈α
contains␈α
one␈α
of␈α
the␈α
most␈α
usable␈α
approaches␈α
to␈α
the
␈↓ ↓Haxiomatization␈αof␈αset␈αtheory.␈αOf␈αcourse,␈αthis␈αcourse␈αis␈αnot␈αconcerned␈αwith␈αthe␈αcontinuum␈αhypothesis
␈↓ ↓Hitself␈α
which␈α
is␈α
Cohen's␈α
main␈α
objective␈α
in␈α
the␈α
book.␈α
Because␈α
the␈α
main␈αemphasis␈αof␈αthe␈αcourse␈αis␈αin
␈↓ ↓Hexpressing␈αfacts␈αabout␈αother␈αmatters␈αwithin␈αlogic,␈αno␈αmathematical␈αbook␈αhas␈αthe␈αright␈αemphasis␈αfor
␈↓ ↓Hour␈α⊃present␈α⊃purposes.␈α⊃We␈α⊂need␈α⊂a␈α⊂new␈α⊂Sylvanus␈α⊂Thompson␈α⊂to␈α⊂write␈α⊂␈↓↓Mathematical␈α⊂Logic␈α⊂for␈α⊂the
␈↓ ↓HPractical␈αMan␈↓.␈αThe␈αelectrical␈α
engineers␈α
are␈α
no␈α
help␈α
here,␈α
because␈α
their␈α
interest␈α
in␈α
logic␈α
concerns␈α
only
␈↓ ↓Hpropositional␈α
logic␈α
whereas␈α
our␈α
main␈α
interest␈α
will␈α
be␈α
in␈α
predicate␈α
calculus.

␈↓ α_5.␈α
Philosophers␈α
have␈α
treated␈α
some␈α
of␈α
the␈α
questions␈α
we␈α
are␈α
interested␈αin␈αhere.␈αTheir␈αpoint␈αof
␈↓ ↓Hview␈αmay␈αbe␈αtypified␈αby␈αthe␈αquestion␈α"What␈αis␈αknowledge"␈αwhereas␈αwe␈αshall␈αbe␈αinterested␈αin␈α"How
␈↓ ↓Hcan␈α⊂we␈α⊂formalize␈α⊂enough␈α⊂about␈α∂knowledge␈α∂so␈α∂that␈α∂we␈α∂can␈α∂express␈α∂facts␈α∂about␈α∂reservation␈α∂clerks
␈↓ ↓Hknowing␈α∩airline␈α∩schedules␈α∩and␈α∩telephone␈α∩numbers␈α∩being␈α∩"in"␈α∩the␈α⊃telephone␈α⊃book.␈α⊃Nevertheless,
␈↓ ↓Hdespite␈αthe␈αdifference␈αin␈αpoint␈αof␈αview,␈αthere␈αis␈αa␈αvast␈αphilosophical␈αliterature␈αwhich␈αis␈αdescribed␈αin
␈↓ ↓Hthe␈α
last␈α
section␈α
of␈α
␈↓↓Some␈α
Philosophical␈α
Problems␈α
from␈α
the␈α
standpoint␈α
of␈α
Artificial␈α
Intelligence.␈↓