[PPT] - Choueiry AIMA: Chapter 7 (Setions 7.1, 7.2, and 7.3) In PowerPoint Presentation

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Title: Logi al Agen ts AIMA: Chapter 7 (Se tions 7.1, 7.2, and 7.3) In tro du tion to Arti ial In telligen e CSCE 476-876, Spring 2016 URL:

www. se.unl.edu/~

ho uei ry/ S1 6-4 76- 87 6 Berthe Y. Choueiry (Sh u-w e-ri) (402)472-5444 B.Y. Choueiry 1 Instru tor's notes #11 Mar h 16, 2016

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Outline

W

umpus w

rld:

motiv ating example

Kno

wledge bases

Logi

for Kno wledge Represen tation & Reasoning

Syn

tax

Seman

ti s

Inferen e

me hanisms:

mplexit

y ,

mpleteness

Prop

sitional

logi /sen ten tial logi Predi ate logi /rst-order logi B.Y. Choueiry 2 Instru tor's notes #11 Mar h 16, 2016

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Motiv ating example: The W umpus w

rld

Early

mputer

game Agen t explores a a v e with:

b
ttomless

pits

a

b east that eats an y

ne

who en ters the ro

m,

and

heap
f

gold to trap

Breeze Breeze Breeze Breeze Breeze

Stench Stench

Breeze

PIT PIT PIT

1 2 3 4 1 2 3 4

START

Gold

Stench

B.Y. Choueiry 3 Instru tor's notes #11 Mar h 16, 2016

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PEAS des ription

f

the W umpus w

rld

P erforman e measure: gold +1000, death

1000,
1

p er step,

10

for using the arro w En vironmen t: Squares adja en t to W umpus are smelly Squares adja en t to pit are breezy Glitter i gold is in the same square Sho

ting

kills W umpus if y

u

are fa ing it Sho

ting

uses up the

nly

arro w Grabbing pi ks up gold if in same square Releasing drops the gold in same square Sensors: Breeze, Glitter, Smell A tuators: Left turn, Righ t turn, F

rw

ard, Grab, Release, Sho

t

B.Y. Choueiry 4 Instru tor's notes #11 Mar h 16, 2016

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W umpus W

rld:

Chara terization Is the w

rld:
Observ

able? No,

nly

lo al p er eption

Deterministi ?

Y es,

ut ome

exa tly sp e ied

Episo

di ? No, sequen tial at the lev el

f

a tions

Stati ?

Y es, W umpus/Pits don't mo v e

Dis rete?

Y es

Single-agen

t? Y es, W umpus

nsidered

a natural feature B.Y. Choueiry 5 Instru tor's notes #11 Mar h 16, 2016

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Empiri al ev aluations: single/m ultiple

nguration

An agen t an do w ell in a single en vironmen t: learns the en vironmen t, exe utes rules. Agen t m ust b e tested in a

mplete

lass

f

en vironmen ts and its a v erage p erforman e m ust b e determined → empiri al exp erimen ts

Constrain

ts: start from p

sition

[1,1℄, limited to 4×4 grid

Lo

ation

f

W umpus and Gold hosen randomly with a uniform distribution (all squares are p

ssible

ex ept [1,1℄)

Ea

h square, ex ept [1,1℄, an b e a pit with probabilit y 0.2

T

erribly bad ases: gold in a pit

r

surrounded b y pits B.Y. Choueiry 6 Instru tor's notes #11 Mar h 16, 2016

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W umpus W

rld:

A ting & Reasoning

After

re eiving initial p er epts, agen t kno ws it is in [1,1℄ and it is OK

No

sten h

r

breeze in [1,1℄ ⇒ [1,2℄ and [2,1℄ are danger-free

Cautious

agen t mo v es

nly

to square it kno ws it is OK

Agen

t mo v es

nly

to square [2,1℄, dete ts breeze y ⇒ ∃ a pit in neigh b

ring

squares [1,1℄, [2,2℄ and [3,1℄. Agen t kno ws no pit in [1,1℄ → Pit indi ated in [2,2℄ and [3,1℄ with P?

Not

visited OK squares? Only [1,2℄. Agen t go es to [1,1℄, pro eeds to [1,2℄ B.Y. Choueiry 7 Instru tor's notes #11 Mar h 16, 2016

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W umpus W

rld:

A ting & Reasoning

Breeze Breeze Breeze Breeze Breeze Stench Stench Breeze

PIT PIT PIT

1 2 3 4 1 2 3 4 START

Gold Stench

A B G P S W = Agent = Breeze = Glitter, Gold = Pit = Stench = Wumpus OK = Safe square V = Visited A OK 1,1 2,1 3,1 4,1 1,2 2,2 3,2 4,2 1,3 2,3 3,3 4,3 1,4 2,4 3,4 4,4 OK OK B P? P? A OK OK OK 1,1 2,1 3,1 4,1 1,2 2,2 3,2 4,2 1,3 2,3 3,3 4,3 1,4 2,4 3,4 4,4 V

(a) (b)

B.Y. Choueiry 8 Instru tor's notes #11 Mar h 16, 2016

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W umpus W

rld:

A ting & Reasoning

Agen

ts dete ts sten h in [1,2℄ ⇒ W umpus nearb y! P

ssibilities:

[1,1℄, [1,3℄

r

[2,2℄. Agen t kno ws [1,1℄ is W umpus-free (Agen t w as there!) Agen t an infer [2,2℄ is W umpus-free ( ∃ sten h in [2,1℄) Agen t infers W umpus is in [1,3℄ (W!)

La

k

f

breeze in [1,2℄ ⇒ [2,2℄ is pit-free But, ∃ a pit in either [2,2℄

r

[3,1℄ ⇒ ∃ pit in [3,1℄ (P!) Inferen e

m

bines kno wledge gained at dieren t times and pla es, b ey

nd

the abilities

f

most animals, but Logi al Inferen e an handle this

Sin e

[2,2℄ is OK and not visited, Agen t mo v es there

et .

B.Y. Choueiry 9 Instru tor's notes #11 Mar h 16, 2016

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W umpus W

rld:

A ting & Reasoning

Breeze Breeze Breeze Breeze Breeze Stench Stench Breeze

PIT PIT PIT

1 2 3 4 1 2 3 4 START

Gold Stench

B B P! A OK OK OK 1,1 2,1 3,1 4,1 1,2 2,2 3,2 4,2 1,3 2,3 3,3 4,3 1,4 2,4 3,4 4,4 V OK W! V P! A OK OK OK 1,1 2,1 3,1 4,1 1,2 2,2 3,2 4,2 1,3 2,3 3,3 4,3 1,4 2,4 3,4 4,4 V S OK W! V V V B S G P? P?

(b) (a)

S A B G P S W = Agent = Breeze = Glitter, Gold = Pit = Stench = Wumpus OK = Safe square V = Visited

B.Y. Choueiry 10 Instru tor's notes #11 Mar h 16, 2016

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The p

in

t

f

the W umpus w

rld

In ea h ase where the agen t dra ws a

n lusion

from the a v ailable information, that

n lusions

is guaran teed to b e

rre t

if the a v ailable information is

rre t.

− →

F undamen tal prop ert y

f

logi al reasoning. B.Y. Choueiry 11 Instru tor's notes #11 Mar h 16, 2016

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Kno wledge Base A fa t in the w

rld:

A represen tation

f

a fa t in the w

rld

A sen ten e= a represen tation

f

a fa t in the w

rld

in a formal language A Kno wledge Based (KB): A set sen ten es A set (of represen tations)

f

fa ts ab

ut

the w

rld

Issues: A ess to KB, Represen tation (language), Reasoning (inferen e) B.Y. Choueiry 12 Instru tor's notes #11 Mar h 16, 2016

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Lev el

f

Kno wledge Agen ts an b e view ed at v arious lev els: 1. Epistemologi al: Abstra t des ription

f

what the agen t kno ws ab

ut

the w

rld

2. Logi al: En o ding

f

kno wledge in to sen ten es 3. Implemen tation: A tual implemen tation (lists, arra ys, hash tables, et .)

V

ery imp

rtan

t for p erforman e

f

agen t

Irrelev

an t for higher lev els

f

kno wledge B.Y. Choueiry 13 Instru tor's notes #11 Mar h 16, 2016

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A simple KB-agen t

function KB-AGENT( percept) returns an action static: KB, a knowledge base t, a counter, initially 0, indicating time TELL(KB, MAKE-PERCEPT-SENTENCE(percept, t)) action

ASK(KB, MAKE-ACTION-QUERY(t))

TELL(KB, MAKE-ACTION-SENTENCE(action, t)) t

t + 1

return action

The agen t m ust b e able to: represen t states, a tions, et . in orp

rate

new p er epts up date in ternal represen tations

f

the w

rld

dedu e hidden prop erties

f

the w

rld

dedu e appropriate a tions B.Y. Choueiry 14 Instru tor's notes #11 Mar h 16, 2016

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Kno wledge-Based Agen t

function KB-AGENT( percept) returns an action static: KB, a knowledge base t, a counter, initially 0, indicating time TELL(KB, MAKE-PERCEPT-SENTENCE(percept, t)) action

ASK(KB, MAKE-ACTION-QUERY(t))

TELL(KB, MAKE-ACTION-SENTENCE(action, t)) t

t + 1

return action

P er eiv es: T ells KB ab

ut

new p er epts (new sen ten es) Represen tation: Make-Per ept-Senten e A ess to KB: Asks KB ab

ut

a tions to tak e (inferen e) T w

primitiv

es: Ask and Tell hide reasoning details A ts: T ells KB ab

ut

a tions (new sen ten es) Represen tation: Make-A tion-Senten e, Make-A tion-Quer y B.Y. Choueiry 15 Instru tor's notes #11 Mar h 16, 2016

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Logi in general Logi s are formal languages for represen ting information su h that

n lusions

an b e dra wn Syn tax denes the sen ten es in the language (grammar) Seman ti s dene the meaning

f

sen ten es; i.e., dene truth

f

a sen ten e in a w

rld

Example: the language

f

arithmeti

Syn

tax: x + 2 ≥ y is a sen ten e; x2 + y > is not a sen ten e

Seman

ti s: x + 2 ≥ y is true i the n um b er x + 2 is no less than the n um b er y x + 2 ≥ y is true in a w

rld

where x = 7, y = 1 x + 2 ≥ y is false in a w

rld

where x = 0, y = 6 B.Y. Choueiry 16 Instru tor's notes #11 Mar h 16, 2016

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T yp es

f

logi Logi s are hara terized b y what they

mmit

to as primitiv es On tologi al

mmitmen

t : what existsfa ts?

b

je ts? time? b eliefs? Epistemologi al

mmitmen

t : what states

f

kno wledge?

Language Ontological Commitment Epistemological Commitment (What exists in the world) (What an agent believes about facts) Propositional logic facts true/false/unknown First-order logic facts, objects, relations true/false/unknown Temporal logic facts, objects, relations, times true/false/unknown Probability theory facts degree of belief 0…1 Fuzzy logic degree of truth degree of belief 0…1

B.Y. Choueiry 17 Instru tor's notes #11 Mar h 16, 2016

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Kno wledge represen tation & reasoning

Follows Sentences Facts Sentence Fact Entails

Semantics Semantics

Representation World

F a ts: in the w

rld

Represen tations: in the

mputer

Reasoning: pro ess

f
nstru ting

new represen tations from

ld
nes

Prop er Reasoning: ensures new represen tations

rresp
nd

to fa ts that a tually follo w from fa ts in the w

rld

B.Y. Choueiry 18 Instru tor's notes #11 Mar h 16, 2016

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En tailmen t En tailmen t means that

ne

thing follo ws from another: (KB |

= α )

Kno wledge base KB en tails sen ten e α i α is true in all w

rlds

where KB is true Example: KB: {a ∧ b}, then KB |

= a;

KB |

= b;

KB |

= a ∨ b

En tailmen t is a relationship b et w een sen ten es (i.e., syn tax) that is based

n

seman ti s (α |

= β

): the truth

f β
n

tains the truth

f α

F

r

example: (x + y = 4) |

= (4 = x + y), (x + y = 4) | = (4 ≥ x + y), (x + y ≥ 4) | = (4 = x + y),

B.Y. Choueiry 19 Instru tor's notes #11 Mar h 16, 2016

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Mo dels Logi ians t ypi ally think in terms

f

mo dels, whi h are formally stru tured w

rlds

with resp e t to whi h truth an b e ev aluated W e sa y m is a mo del

f

a sen ten e α if α is true in m

M(α)

is the set

f

all mo dels

f α

Then KB |

= α

if and

nly

if M(KB) ⊆ M(α)

M( )

α M(KB)

B.Y. Choueiry 20 Instru tor's notes #11 Mar h 16, 2016

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En tailmen t in the W umpus w

rld

Situation: Agen t dete ted nothing in [1,1℄, breeze in [2,1℄ 23 =8 p

ssible

mo dels P er epts + the PEAS des ription = KB Agen t w

nders

whether pit is in [1,2℄, [2,2℄, and [3,1℄: Only 3 mo dels where the KB is true

α1

= no pit in [1,2℄:

α1

is true in 4 mo dels.

1 2 3 1 2 PIT 1 2 3 1 2 PIT 1 2 3 1 2 PIT PIT PIT 1 2 3 1 2 PIT PIT 1 2 3 1 2 PIT 1 2 3 1 2 PIT PIT 1 2 3 1 2 PIT PIT 1 2 3 1 2

KB

α1

B r ee z e B r e e z e B r e e z e B r e e z e B r e e z e B r e e z e B r e e z e B r e e z e B.Y. Choueiry 21 Instru tor's notes #11 Mar h 16, 2016

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En tailmen t in the W umpus w

rld

1 2 3 1 2

PIT

1 2 3 1 2

PIT

1 2 3 1 2

PIT PIT PIT

1 2 3 1 2

PIT PIT

1 2 3 1 2

PIT

1 2 3 1 2

PIT PIT

1 2 3 1 2

PIT PIT

1 2 3 1 2

KB

α1

B r e e z e B r e e z e B r ee z e B r ee z e B r ee z e B r e e z e B r e e z e B r ee z e

Consider: α1 = no pit in [1,2℄, α2 = no pit in [2,2℄ Mo del he king: KB |

= α1

, KB |

= α2

Giv en KB, agen t annot

n lude

whether α2 holds

r

not En tailmen t an b e used to deriv e

n lusions:

Inferen e Inferen e here is done b y mo del he king B.Y. Choueiry 22 Instru tor's notes #11 Mar h 16, 2016

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Inferen e KB ⊢i α ≡ α is deriv ed from KB b y pro edure i Consequen es

f

KB are a ha ysta k; α is a needle. En tailmen t = needle in ha ysta k; inferen e = nding it Soundness: i is sound if whenev er KB ⊢i α , it is also true that KB |

= α

Completeness: i is

mplete

if whenev er KB |

= α

, it is also true that KB ⊢i α That is, the pro edure will answ er an y question whose answ er follo ws from what is kno wn b y the KB The re ord

f
p

eration

f

a sound inferen e pro edure is a pro

f

Next, prop

sitional

logi : syn tax, seman ti s, and inferen e B.Y. Choueiry 23 Instru tor's notes #11 Mar h 16, 2016