7 LOGICAL AGENTS

2 INTELLIGENT AGENTS

function TABLE-DRIVEN-AGENT( ) returns an action static: , a sequence, initially empty

, a table of actions, indexed by percept sequences, initially fully specified append to the end of

LOOKUP( , ) return

Figure 2.8

function REFLEX-VACUUM-AGENT( [ , ^!" ]) returns an action if ^!" =^{# $ %} then return^{& !'}

else if⁽ =⁾ then return^{* (+,} else if⁽ =^- then return^{. 0/}

Figure 2.10

function SIMPLE-REFLEX-AGENT( ) returns an action static: ^!1, a set of condition–action rules

2 INTERPRET-INPUT( )

!12 RULE-MATCH( ³ ,^!" ) RULE-ACTION[^!1 ] return

Figure 2.13

2

function REFLEX-AGENT-WITH-STATE( ) returns an action static: ³ , a description of the current world state

!1 , a set of condition–action rules , the most recent action, initially none

2 UPDATE-STATE( ³ , , )

!12 RULE-MATCH( ³ ,^!" ) RULE-ACTION[^!1 ] return

Figure 2.16

3 SOLVING PROBLEMS BY SEARCHING

function SIMPLE-PROBLEM-SOLVING-AGENT(⁴ ) returns an action inputs:⁴ , a percept

static: ⁵, an action sequence, initially empty

3 , some description of the current world state

+, a goal, initially null

6 , a problem formulation

2 UPDATE-STATE( ³ , ) if ⁵ is empty then do

+ FORMULATE-GOAL( )

4 67 FORMULATE-PROBLEM( ³ ,⁺)

58 SEARCH(⁶ ) FIRST( ⁵ )

59 REST(⁵) return

Figure 3.2

function TREE-SEARCH(⁶ , ^3+% ) returns a solution, or failure initialize the search tree using the initial state of⁶

loop do

if there are no candidates for expansion then return failure choose a leaf node for expansion according to ^3+%

if the node contains a goal state then return the corresponding solution else expand the node and add the resulting nodes to the search tree

Figure 3.9

4

function TREE-SEARCH(^6;:0/$1+ ) returns a solution, or failure

/0+1<

INSERT(MAKE-NODE(INITIAL-STATE[⁶ ]),^/$1+ ) loop do

if EMPTY?(^/$+1 ) then return failure

=2 REMOVE-FIRST(^/0+1 )

if GOAL-TEST[⁶ ] applied to STATE[^>=] succeeds then return SOLUTION(⁼ )

/$1+<

INSERT-ALL(EXPAND(⁼ ,⁶ ),^/$1+ ) function EXPAND(^>=:6 ) returns a set of nodes

!? the empty set

for each^@ , ^{!1 A} in SUCCESSOR-FN[⁶ ](STATE[^>= ]) do

B a new NODE

STATE[]^{C !1} PARENT-NODE[ ]^D>=

ACTION[]^E

PATH-COST[] PATH-COST[⁼ ] + STEP-COST(^>=, , ) DEPTH[ ] DEPTH[⁼ ] + 1

add to^!

return^!

Figure 3.12

function DEPTH-LIMITED-SEARCH(^{4 6} ,^06F$ ) returns a solution, or failure/cutoff return RECURSIVE-DLS(MAKE-NODE(INITIAL-STATE[⁶ ]),⁶ ,^$6F$ ) function RECURSIVE-DLS(^>= ,⁶ ,^$6F$ ) returns a solution, or failure/cutoff

!1 G !1 =H2

false

if GOAL-TEST[⁶ ](STATE[^>=]) then return SOLUTION(⁼ ) else if DEPTH[^>= ] =^06F$ then return^{!" 3IG}

else for each^! in EXPAND(⁼ ,⁶ ) do

!1J 4

RECURSIVE-DLS(^! ,⁶ ,^$6F$ ) if ^!1 =^{!1 IG} then^{!1 IG !1 =H2} true else if ^{!1 LKM /$!1} then return ^!"

if^{!1 IG !1 =H} then return^{!" 3IG} else return^/$!1

Figure 3.17

6 Chapter 3. Solving Problems by Searching

function ITERATIVE-DEEPENING-SEARCH(⁶ ) returns a solution, or failure inputs:⁶ , a problem

for^{= 0,N} 0 to^O do

!1J 4

DEPTH-LIMITED-SEARCH(⁶ ,^{=4 ,} ) if ^{!1 LKM} cutoff then return^!1J

Figure 3.19

function GRAPH-SEARCH(^6P:0/$1+ ) returns a solution, or failure

( =Q an empty set

/0+1<

INSERT(MAKE-NODE(INITIAL-STATE[⁶ ]),^/$1+ ) loop do

if EMPTY?(^/$+1 ) then return failure

=2 REMOVE-FIRST(^/0+1 )

if GOAL-TEST[⁶ ](STATE[⁼ ]) then return SOLUTION(^>= ) if STATE[⁼ ] is not in^{( =} then

add STATE[^>= ] to^{( =}

/$1+<

INSERT-ALL(EXPAND(⁼ ,^{4 6} ),^/$1+ )

Figure 3.25

function RECURSIVE-BEST-FIRST-SEARCH(⁶ ) returns a solution, or failure RBFS(⁶ , MAKE-NODE(INITIAL-STATE[⁶ ]),^O )

function RBFS(⁶ ,^>= ,^{/ $6F0} ) returns a solution, or failure and a new^R -cost limit if GOAL-TEST[⁶ ]( ³ ) then return^>=

!? EXPAND(⁼ ,⁶ ) if ^!4 is empty then return^/$!" ,^O for each in^! do

R [s]TSVUWYX0Z>XI[]\_^]XI[:

R2`

=a0[

repeat

4 the lowest^R -value node in^! if^{R2` acbC/ J$6F$} then return^/$J!1 ,^R [ ]

J > $de2

the second-lowest^R -value among^!

!1J

,^R [ ] RBFS(^{4 6} , ,^{Sgf(h?X/ 06F$ :i $d[}) if ^{!1 LKM /$!1} then return ^!"

Figure 4.6

function HILL-CLIMBING(⁶ ) returns a state that is a local maximum inputs:⁶ , a problem

local variables: ^!14 , a node

>(+,"

, a node

!1 4

MAKE-NODE(INITIAL-STATE[⁶ ]) loop do

>(+," 8

a highest-valued successor of^!1

if VALUE[neighbor]^j VALUE[current] then return STATE[^{!1 4} ]

!14 4DY+,

Figure 4.13

8 Chapter 4. Informed Search and Exploration

function SIMULATED-ANNEALING(⁶ ,^{, =!1} ) returns a solution state inputs:⁶ , a problem

,=!1 , a mapping from time to “temperature”

local variables: ^!14 , a node

>k

, a node

l

, a “temperature” controlling the probability of downward steps

!1 4

MAKE-NODE(INITIAL-STATE[⁶ ]) for ⁴ 1 to^O do

l

C, =!"

[ ]

if ^l = 0 then return^{!" 4}

>k

a randomly selected successor of^{!" 4}

mon

VALUE[^>k ] – VALUE[^{!" 4} ] if

mgn

b 0 then^{!14 4DY k}

else^{!14 4DY k} only with probability^piq2rBsIt

Figure 4.17

function GENETIC-ALGORITHM(^"!1 , FITNESS-FN) returns an individual inputs:^"!1 , a set of individuals

FITNESS-FN, a function that measures the fitness of an individual repeat

>u "!1(

empty set

loop for from 1 to SIZE(^"!1 ) do

kv RANDOM-SELECTION("4!"(

, FITNESS-FN)

%w RANDOM-SELECTION(^"!1( , FITNESS-FN)

,$=Q REPRODUCE(^k ,^% )

if (small random probability) then^,$(=v MUTATE(^,0(= ) add^,$(= to^{Yu "!1(}

"!1 xC>u "!1(

until some individual is fit enough, or enough time has elapsed return the best individual in^"!1 , according to FITNESS-FN

function REPRODUCE(^k ,^% ) returns an individual inputs:^k ,^% , parent individuals

LENGTH(^k )

< random number from 1 to

return APPEND(SUBSTRING(^k , 1, ), SUBSTRING(^% ,^y\{z , ))

Figure 4.21

function ONLINE-DFS-AGENT( ) returns an action inputs: ^|, a percept that identifies the current state

static: ^!1 , a table, indexed by action and state, initially empty

!1Y k( =

, a table that lists, for each visited state, the actions not yet tried

!1Y e' 'e =

, a table that lists, for each visited state, the backtracks not yet tried

, , the previous state and action, initially null if GOAL-TEST( ^|) then return

if ^| is a new state then^{!1Yk( =} [ ^|] ACTIONS( ^|) if is not null then do

!1J

[ ,]^{D |}

add to the front of!1Y e' 'e =

[ ^|] if!1>k4 =

[ ^|] is empty then if!1Y e' 'e =

[ ^|] is empty then return

else^w an action such that ^!1 [ , ^|] = POP(!1Y e' 'e =

[ ^|]) else^L POP(^{!1Y k( =} [ ^|])

<D |

return

Figure 4.25

function LRTA*-AGENT( ^|) returns an action inputs: ^|, a percept that identifies the current state

static: ^!1 , a table, indexed by action and state, initially empty

}

, a table of cost estimates indexed by state, initially empty

, , the previous state and action, initially null if GOAL-TEST( ^|) then return

if ^| is a new state (not in^} ) then^} [ ^|]^{~^} ( ^|) unless is null

!1J

[ ,]^{D |}

}

[ ] ^Sofh

€ ACTIONS^‚Iƒ

LRTA*-COST( ,, ^!" [,],^} )

L an action in ACTIONS(^|) that minimizes LRTA*-COST(^|, , ^!1 [ ,^|],^} )

<D

|

return

function LRTA*-COST( , , ^|,^} ) returns a cost estimate if ^| is undefined then return^{^?X3„i[}

else return^{X3„e: †:„ |[g\ˆ‡ `„ |a}

Figure 4.29

5 ^CONSTRAINT SATISFACTION PROBLEMS

function BACKTRACKING-SEARCH( ) returns a solution, or failure return RECURSIVE-BACKTRACKING(^‰9Š , )

function RECURSIVE-BACKTRACKING( ^(+e46g4 ,³ ) returns a solution, or failure if^(+e6g4 is complete then return ^(+e46g4

d8 SELECT-UNASSIGNED-VARIABLE(VARIABLES[³ ],^(+e6g4 , ) for each^dJ!4 in ORDER-DOMAIN-VALUES(^d , ^+46g4 , ) do

if^dJ!4 is consistent with ^+46g4 according to CONSTRAINTS[³ ] then add^{‰ d} =^{d!4 Š} to^(+e6g

!1J 4

RECURSIVE-BACKTRACKING(^(+e6g ,³ ) if^{!1J LKM /$J!1} then return ^!1

remove^{‰ d} =^{d!4 Š} from^(+46g return^/$J!1

Figure 5.4

10

function AC-3(³ ) returns the CSP, possibly with reduced domains inputs:³ , a binary CSP with variables^{‰i‹Œ : ‹gŽ :: ‹o‘Š}

local variables: ^5!4!4, a queue of arcs, initially all the arcs in³ while^5!4! is not empty do

X

‹o’

:

‹F“

[4 REMOVE-FIRST(^5!4!4 )

if REMOVE-INCONSISTENT-VALUES(^{‹ ’: ‹ “} ) then for each^‹V” in NEIGHBORS[^‹o’] do

add (^{‹c” : ‹ ’}) to^5!4!4

function REMOVE-INCONSISTENT-VALUES(^{‹ ’: ‹ “} ) returns true iff we remove a value

6od =v•/

for each^k in DOMAIN[^{‹ ’}] do

if no value^– in DOMAIN[^{‹ “}] allows (^k ,^% ) to satisfy the constraint between^{‹ ’} and^{‹ “} then delete^k from DOMAIN[^{‹ ’}]; 6od =vD !4

return ^{6od =}

Figure 5.9

function MIN-CONFLICTS( ,^6oik ) returns a solution or failure inputs:³ , a constraint satisfaction problem

6oik , the number of steps allowed before giving up

!1 4

an initial complete assignment for for = 1 to^6oik do

if^!1 is a solution for then return^!14

d8 a randomly chosen, conflicted variable from VARIABLES[ ]

d!<

the value^d for^d that minimizes CONFLICTS(^d ,^d ,^{!1 4} ,³ ) set^{d M dJ!4} in ^{!" 4}

return^/$J!1

Figure 5.11

6 ADVERSARIAL SEARCH

function MINIMAX-DECISION( ) returns^— inputs: , current state in game

dw MAX-VALUE(state)

return the in SUCCESSORS( ³ ) with value^d function MAX-VALUE( ) returnsF!1 $J$ %˜dJ!4

if TERMINAL-TEST( ) then return UTILITY( )

dwC™

O

for^4: in SUCCESSORS( ³ ) do

dw MAX(v, MIN-VALUE( )) return^d

function MIN-VALUE( ³ ) returns^{x!1 $0 %˜dJ!4} if TERMINAL-TEST( ) then return UTILITY( )

dw

O

for^4: in SUCCESSORS( ³ ) do

dw MIN(v, MAX-VALUE( )) return^d

Figure 6.4

12

function ALPHA-BETA-SEARCH( ) returns an action inputs: , current state in game

dw MAX-VALUE( ,^{™ O} ,^{\ O} )

return the in SUCCESSORS( ³ ) with value^d function MAX-VALUE( ,^š ,^› ) returnsx!" $J$ %Fd!4

inputs: , current state in game

š , the value of the best alternative for MAXalong the path to

› , the value of the best alternative for MINalong the path to if TERMINAL-TEST( ) then return UTILITY( )

dwC™

O

for^4: in SUCCESSORS( ³ ) do

dw MAX(v, MIN-VALUE( ,^š ,^› )) if^œžŸ› then return^d

š

MAX(^š , v) return^d

function MIN-VALUE( ³ ,^š ,^› ) returns^{F!1 $$ %˜d!} inputs: , current state in game

š , the value of the best alternative for MAXalong the path to

› , the value of the best alternative for MINalong the path to if TERMINAL-TEST( ) then return UTILITY( )

dw~\

O

for^4: in SUCCESSORS( ³ ) do

dw MIN(v, MAX-VALUE( ,^š ,^› )) if^œžj š then return^d

›

MIN(^› , v) return^d

Figure 6.9

7 LOGICAL AGENTS

function KB-AGENT( ) returns an static:^¡¢- , a knowledge base

, a counter, initially 0, indicating time TELL(^¡¢- , MAKE-PERCEPT-SENTENCE( , ))

ASK(^¡¢- , MAKE-ACTION-QUERY( )) TELL(^¡¢- , MAKE-ACTION-SENTENCE( , ))

D + 1 return

Figure 7.2

function TT-ENTAILS?(^¡¢- ,^š ) returns ^!4 or^/J

inputs:^¡¢- , the knowledge base, a sentence in propositional logic

š , the query, a sentence in propositional logic

%6g 2

a list of the proposition symbols in^¡¢- and^š return TT-CHECK-ALL(^¡N- ,^š ,^%6g ,^`a)

function TT-CHECK-ALL(^¡¢- ,^š ,^%6g ,^6o=) returns ^!4 or^/ if EMPTY?(^%6g ) then

if PL-TRUE?(^¡N- ,^6o=) then return PL-TRUE?(^š ,^6o=) else return ^!4

else do

£

FIRST(^%6g ); ⁴ REST(^%6g )

return TT-CHECK-ALL(^¡¢- ,^š , , EXTEND(^{£ : !4e:6o=}) and TT-CHECK-ALL(^¡¢- ,^š , , EXTEND(^{£ :0/J:6o=})

Figure 7.12

14

function PL-RESOLUTION(^¡¢- ,^š ) returns ^!4 or^/

inputs:^¡¢- , the knowledge base, a sentence in propositional logic

š , the query, a sentence in propositional logic

(!1B the set of clauses in the CNF representation of^{¡¢-_¤P¥9š}

Yu¦

‰9Š

loop do

for each^{§ ’},^{§ “} in^(!1 do

Jd4 B

PL-RESOLVE(^{§ ’},^{§ “} )

if^de4 contains the empty clause then return ^!4

Yu¦DYu—¨© de

if^Yu«ª•(!1 then return^/

!"<¬(!1?¨cYu

Figure 7.15

function PL-FC-ENTAILS?(^¡¢- ,⁵ ) returns ^!4 or^/

inputs:^¡¢- , the knowledge base, a set of propositional Horn clauses

5 , the query, a proposition symbol

local variables: ^!14 , a table, indexed by clause, initially the number of premises

$/ =

, a table, indexed by symbol, each entry initially^/J

+1= , a list of symbols, initially the symbols known to be true in^¡¢- while^+>=e is not empty do

­ POP(^+1>= ) unless^{0/ =} [ ] do

$/ =

[ ]^{C !4}

for each Horn clause in whose premise appears do decrement^!14 [ ]

if^!" [ ] = 0 then do

if HEAD[ ] =⁵ then return ^!4 PUSH(HEAD[ ],^+1>= ) return^/

Figure 7.18

16 Chapter 7. Logical Agents

function DPLL-SATISFIABLE?( ) returns ^!4 or^/ inputs: , a sentence in propositional logic

(!1B the set of clauses in the CNF representation of

%6g 2

a list of the proposition symbols in return DPLL(^!1 , ^{%6g J},^`a)

function DPLL(^(!1 ,^%6g ,^6o=) returns ^! or^/J if every clause in^(!1 is true in^6o= then return ^!4 if some clause in^!1 is false in^6o= then return^/J

®

,^dJ!42 FIND-PURE-SYMBOL(^%6gJ ,^!",^6o=)

if^® is non-null then return DPLL(^(!1 , ^{%6g J} –^® , EXTEND(^{£ :dJ!4:6o=})

®

,^dJ!42 FIND-UNIT-CLAUSE(^(!1 ,^6o=)

if^® is non-null then return DPLL(^(!1 , ^{%6g J} –^® , EXTEND(^{£ :dJ!4:6o=})

®

FIRST(^%6g ); ⁴ REST(^%6gJ)

return DPLL(^!1 , , EXTEND(^® , ^!4 ,^6o=)) or DPLL(^!1 , , EXTEND(^® ,^/ ,^6o=))

Figure 7.21

function WALKSAT(^(!1, ,^{6oik ¯y} ) returns a satisfying model or^/$J!1 inputs:^(!1 , a set of clauses in propositional logic

, the probability of choosing to do a “random walk” move, typically around 0.5

6oik ¯y

, number of flips allowed before giving up

6o=e a random assignment of ^!4 /^/ to the symbols in^(!1 for ^{M z} to^{6oik ¯y4} do

if^6o= satisfies^!1 then return^6o=

!"2

a randomly selected clause from^(!1 that is false in^6o=

with probability flip the value in^6o= of a randomly selected symbol from^(!1 else flip whichever symbol in^!1 maximizes the number of satisfied clauses return^/$J!1

Figure 7.23

function PL-WUMPUS-AGENT( ) returns an inputs:⁴ , a list, [ ^>, , ^°i ,^+e$ ]

static:^¡¢- , a knowledge base, initially containing the “physics” of the wumpus world

k ,^% ,^{34 3} , the agent’s position (initially 1,1) and orientation (initially^(+, )

di$$ =

, an array indicating which squares have been visited, initially^/ , the agent’s most recent action, initially null

( , an action sequence, initially empty update^k ,^% ,⁴ ,^{di$$ =} based on ^e if ^, then TELL(^¡¢- ,^±?²³´ ) else TELL(^¡¢- ,^{¥—±]²³´} ) if ^°i then TELL(^¡¢- ,^µN²³´ ) else TELL(^¡¢- ,^{¥—µ¢²³´} )

if^+J$ then ^­~+

else if⁴ is nonempty then POP(⁽ )

else if for some fringe square [,^¶ ], ASK(^¡¢- ,^{X¥ £ ’³“ ¤T¥—· ’³“ [}) is ^!4 or for some fringe square [,^¶ ], ASK(^¡¢- ,^{X£ ’³“¸ · ’³“ [}) is^/J then do

4 A*-GRAPH-SEARCH(ROUTE-PROBLEM([^k ,^% ],^{34 3} , [,^¶ ],^{di$$ =} ))

e ­ POP(⁽ )

else a randomly chosen move return

Figure 7.26

8 FIRST-ORDER LOGIC

18

function UNIFY(^k ,^% ,^¹ ) returns a substitution to make^k and^% identical inputs:^k , a variable, constant, list, or compound

% , a variable, constant, list, or compound

¹ , the substitution built up so far (optional, defaults to empty) if^¹ = failure then return failure

else if^k =^% then return^¹

else if VARIABLE?(^k ) then return UNIFY-VAR(^k ,^% ,^¹ ) else if VARIABLE?(^% ) then return UNIFY-VAR(^% ,^k ,^¹ ) else if COMPOUND?(^k ) and COMPOUND?(^% ) then

return UNIFY(ARGS[^k ], ARGS[^% ], UNIFY(OP[^k ], OP[^% ],^¹ )) else if LIST?(^k ) and LIST?(^% ) then

return UNIFY(REST[^k ], REST[^% ], UNIFY(FIRST[^k ], FIRST[^% ],^¹ )) else return failure

function UNIFY-VAR(^d ,^k ,^¹ ) returns a substitution inputs:^d, a variable

k , any expression

¹ , the substitution built up so far if^{‰ dº1dŠ¦»7¹} then return UNIFY(^d,^k ,^¹ ) else if^{‰¼ º"dŠ¦»7¹} then return UNIFY(^d ,^d,^¹ ) else if OCCUR-CHECK?(^d ,^k ) then return failure else return add^{‰ d} /^{k Š} to^¹

Figure 9.2

20 Chapter 9. Inference in First-Order Logic

function FOL-FC-ASK(^¡N- ,^š ) returns a substitution or^/J inputs:^¡¢- , the knowledge base, a set of first-order definite clauses

š , the query, an atomic sentence

local variables:^>u , the new sentences inferred on each iteration repeat until^Yu is empty

>u—

‰9Š

for each sentence in^¡N- do

X

Œ<¤



¤ ‘•½

5[4 STANDARDIZE-APART( )

for each^¹ such that SUBST(^¹ , ^{Œ ¤  ¤ ‘} ) = SUBST(^¹ , ^{|Œ ¤  ¤ ‘|} ) for some ^{|Œ ::I ‘|} in^¡N-

5 |

SUBST(^¹ ,⁵ )

if^{5 |} is not a renaming of some sentence already in^¡¢- or^>u then do add^{5 |} to^Yu

¾

UNIFY(^{5 |},^š ) if

¾

is not^/$ then return

¾

add^Yu to^¡¢- return^/

Figure 9.5

function FOL-BC-ASK(^¡¢- ,^+J ,^¹ ) returns a set of substitutions inputs:^¡¢- , a knowledge base

+

, a list of conjuncts forming a query (^¹ already applied)

¹ , the current substitution, initially the empty substitution^‰9Š

local variables: ^4uy, a set of substitutions, initially empty if⁺ is empty then return^‰¹Š

5 |

SUBST(^¹ , FIRST(⁺ ))

for each sentence in^¡¢- where STANDARDIZE-APART( ) =^{X ŒP¤  ¤ ‘ž½À¿ [} and^{¹ |} UNIFY(⁵ ,^{5 |}) succeeds

>u +JB

` Œ ::I

‘BÁREST(⁺)^a

4uyB FOL-BC-ASK(^¡¢- ,^{Yu +} , COMPOSE(^{¹ |},^¹ ))^¨Â4uy

return^uy

Figure 9.9

procedure APPEND(^k ,^% ,^i° ,^{4 $4!} )

$ GLOBAL-TRAIL-POINTER()

if^k =^`a and UNIFY(^% ,^i° ) then CALL(^{4 $!4} ) RESET-TRAIL( ^$)

L NEW-VARIABLE();^kà NEW-VARIABLE();^°y NEW-VARIABLE()

if UNIFY(^ik , [ —^k ]) and UNIFY(^i° , [ —^° ]) then APPEND(^k ,^% ,^° , ^$4! )

Figure 9.12

procedure OTTER( ,^!" )

inputs:, a set of support—clauses defining the problem (a global variable)

!"

, background knowledge potentially relevant to the problem repeat

clause the lightest member of

move^(!1 from to^!1

PROCESS(INFER(^(!1 ,^!" ), ) until =^`a or a refutation has been found function INFER(^(!1 ,^!1 ) returns clauses

resolve^(!1 with each member of^!"

return the resulting clauses after applying FILTER

procedure PROCESS(^(!1 ,) for each^(!1 in^(!1 do

!"2

SIMPLIFY(^(!1 ) merge identical literals

discard clause if it is a tautology

< [^(!1 —]

if^(!1 has no literals then a refutation has been found if^(!1 has one literal then look for unit refutation

Figure 9.19

10 ^KNOWLEDGE REPRESENTATION

22

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e=]X

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PRECOND:^{) X… :2†1[ ¤Ç)} X(Ì]:<†"[

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… [ ¤ ® (>X(Ì[

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EFFECT:^{¥¦) X… :2†"[ ¤ Ä 2X… :Ì[[}

)

2XÍB4(=]X

:Ì]:2†"[:

PRECOND:^{Ä 2X… :>Ì[ ¤Ç)} X(Ì]:<†1[

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EFFECT:^{) X… :2†"[ ¤T¥}

Ä

2X

:Ì[[

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2X

Å %>X(Ì]:>/6P:y 3[:

PRECOND:⁾ X(Ì?:/ 6c[

¤ ® (>X(Ì[

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$" XI [

EFFECT:^¥¦) X(Ì]:>/6V[

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X(Ì]:y 3[[

Figure 11.3

24 Chapter 11. Planning

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, PRECOND:^{) X& " : l !1'"[}

EFFECT:^{¥¦) X& " e: l !1"'[ ¤Ç) X& " : Ë !1>=[[}

)

2X

*

6odeeX

Å

:

)

k[, PRECOND:^{) XÅ : ) ki[}

EFFECT:^{¥¦) XÅ ( : ) k[ ¤Ç) XÅ ( :}

Ë

!1>=[[

)

2X

®

!1

Æ

2X

&

" :

)

ki[,

PRECOND:^{) X & " : Ë !1>=4[ ¤É¥¦) XÅ ( : ) k[}

EFFECT:^{¥¦) X& " :}

Ë

!"=4[

¤É) X

&

" e:

)

k[[

)

2X

.

d

Æ

d4(+,

, PRECOND:

EFFECT:^{¥¦) X& " : Ë !"=4[ ¤T¥¦) X & " : ) ki[ ¤T¥¦) X& " : l} !""'"[

¤;¥¦) X

Å

:

Ë

!"=4[

¤T¥¦) X

Å

:

)

ki[[

Figure 11.5

Ä

$ X

Æ

<XÎ:

l

[

¤ˆÆ 2X

µ : l i[

¤ˆÆ 2X

§ : l i[

¤É- ('>XÎN[

¤É- ('>X

µ [

¤É- ('>X

§ [

¤ˆÊ

"XÎN[

¤ŸÊ 1X

µ [

¤ˆÊ

"X

§

[[

Ë

X

Æ

2XÎ:

µ [

¤ˆÆ

<X

µ : § [[

)

2XÏÐdeX3Ñi:

¼ : – [:

PRECOND:^{Æ 2X3Ñi: ¼ [ ¤ŸÊ 1X3Ñ[ ¤ˆÊ "X– [ ¤É- '>X3Ñ[ ¤}

X3Ñ{KM

¼ [ ¤ X3ÑKM

– [ ¤ X¼ KM

– [

,

EFFECT:^{Æ <X3Ñi: – [ ¤ˆÊ "X¼ [ ¤T¥_Æ 2X3Ñi: ¼ [ ¤É¥_Ê 1X– [[}

)

2XÏÐde l l

X3Ñi:

¼

[:

PRECOND:^{Æ 2X3Ñi: ¼ [ ¤ŸÊ 1X3Ñ[ ¤É- ('>X3Ñ[ ¤ X3Ñ{KM ¼ [}, EFFECT:^{Æ <X3Ñi: l [ ¤ŸÊ 1X¼ [ ¤T¥_Æ <X3Ñi: ¼ [[}

Figure 11.7

) 2X

*

6odeeX

&

" :

l

!""'"[

, PRECOND:^{) X& " : l !1'"[}

EFFECT:^{¥¦) X & " e: l !1"'[ ¤Ç) X & " : Ë !1>=[[}

)

2X

*

6odeeX

Å

:

)

k[, PRECOND:^{) XÅ : ) ki[}

EFFECT:^{¥¦) XÅ ( : ) k[ ¤Ç) XÅ ( : Ë !1>=[[}

)

2X

®

!1

Æ

2X

&

" :

)

ki[,

PRECOND:^{) X& " : Ë !1>=4[ ¤É¥¦) XÅ ( : ) k[}

EFFECT:^{¥¦) X& " :}

Ë

!"=4[

¤Ç) X

&

" e:

)

ki[[

)

2X

.

d

Æ

d4(+,

, PRECOND:

EFFECT:^{¥¦) X& " : Ë !"=4[ ¤É¥¦) X& " : ) ki[ ¤T¥¦) X& " : l} !""'"[

¤;¥¦) X

Å

:

Ë

!"=4[

¤T¥¦) X

Å

( :

)

ki[[

Figure 11.11

Ä

$ X

}

deeX

Ê

'i[[

Ë

X

}

dX

Ê

'[

¤ n 2X

Ê

i'i[[

)

2X

n

X

Ê

i'i[

PRECOND:^{} dX Ê '[}

EFFECT:^{¥ } deX Ê 'ei[ ¤}

n

2X

Ê

'e[)

)

2X

-

i'X

Ê

'[

PRECOND:^{¥ } dXÊ '[}

EFFECT:^{} deX Ê 'ei[}

Figure 11.16

function GRAPHPLAN(⁶ ) returns solution or failure

+e4,v

INITIAL-PLANNING-GRAPH(⁶ )

+<

GOALS[^{4 6} ] loop do

if^+J all non-mutex in last level of^{+ 4,} then do

!1

EXTRACT-SOLUTION(^+e4, ,⁺ , LENGTH(^+e, )) if^{!" ÐKM /$!1} then return^J!1

else if NO-SOLUTION-POSSIBLE(^{+ 4,} ) then return^/$!1

+4,Ã EXPAND-GRAPH(^{+ 4,} ,⁶ )

Figure 11.19

26 Chapter 11. Planning

function SATPLAN(⁶ ,^l˜Ò2ÓÔ ) returns solution or failure inputs:⁶ , a planning problem

l˜Ò2ÓÔ

, an upper limit for plan length for^l = 0 to ^l˜Ò2ÓÔ do

/ ,^6o$1+Ã TRANSLATE-TO-SAT(⁶ ,^l )

(+46g 4

SAT-SOLVER(^/ ) if ^+46g4 is not null then

return EXTRACT-SOLUTION( ^(+e46g4 ,^6o$+ ) return^/$J!1

Figure 11.22