Laurea in Computer Science Laurea in Computer Science MAGISTRALE MAGISTRALE

(1)

1

Multistrategy Reasoning / 3 Multistrategy Reasoning / 3 Example (legal domain) Example (legal domain)

Laurea in Computer Science Laurea in Computer Science

MAGISTRALE MAGISTRALE

Corso di

ARTIFICIAL INTELLIGENCE Stefano Ferilli

Questi lucidi sono stati preparati per uso didattico. Essi contengono materiale originale di proprietà dell'Università degli Studi di Bari e/o figure di proprietà di altri autori, società e organizzazioni di cui e' riportato il riferimento. Tutto o parte del materiale può essere fotocopiato per uso personale o didattico ma non può essere distribuito per uso commerciale. Qualunque altro uso richiede una specifica autorizzazione da parte dell'Università degli Studi di Bari e degli altri autori coinvolti.

Introduction

●

Artificial Intelligence

●

Representation and Inference

●

Knowledge Representation

●

(First-Order) Logics

●

Ontology

●

Calculus

–Multistrategic Inference

●

Example

●

Conclusions

Artificial Intelligence

●

Intelligent Agents

●

Artificial Intelligence-based Systems

●

Endowed significant levels of autonomy

●

Act in their environment

–

In a satisfactory, rational, flexible way

–

Even in case of partial or uncertain information

–

Exhibiting an intelligent, aware behavior

–

Sometimes showing true experience in the domain in which they operate

Logics

●

Objects → Terms

●

Constants, Variables, Functions

●

Claims → Atoms

●

Predicates applied to terms

●

Composition of Claims → Expressions

●

Logistic Connectives

–NOT …

–… AND …, … XOR …, … OR…

–IF … THEN …, … IF AND ONLY IF …

Logics

●

2 specific kinds of expressions

●

Facts

–

Claims (known or supposed to be) true

●

Rules

–

Laws, based on which, if something is true, something else must necessarily be true, as well

Ontology

●

Defines the kind of things that exist in the application domain

●

“its aim is providing a framework of distinctions that can be exploited to discriminte and classify the things that exist and define the words describing them.”

●

Properties

●

Relationships

–

Subclass, Instance, Meronymy, ...

(2)

Calculus

●

Inference strategies

●

Deduction

–Ontological, Subsumption, Modus Ponens, Modus Tollens, ...

●

Abstraction

●

Abduction

●

Induction

●

Probability

●

Argumentation

●

Analogy

Legal Knowledge Representation

●

Describing an aspect of reality, of behaviors and of norms that regulate them in a way that is:

●

Isomorphic to reality and to norms

●

Formal

●

Updatable

●

‘Neutral’

[D. Tiscornia, Istituto per la Documentazione Giuridica del CNR]

Facts

●

Example

●

Peter held his black Beretta 92 having s/n 1234, which seemingly fired

–hold(peter,object847) s_n(object847,1234) –color(object847,black) bullet_off(object847)?

●

Max is an Italian, he is a fearful guy, he had a heart attack, he is still, prone and does not leave a halo if placing a mirror near his mouth

–fearful(max) [0.98] italian(max) –has_heart_attack(max) still(max)

–prone(max) leave_halo(max,mirror)

Rules

●

Norm

●

Whoever causes death to a man is punished with imprisonment for no less than 21 years

–

 x:Man, y:Man : causes(x,y,Death) 

punishment(x,imprisonment,21,)

Scientific Rules

●To whoever dies due to suffering a heart attack because he was frightened by something, that something caused death by heart attack

● x:Man, y:Man :

frighten(x,y)  has_heart_attack(y)  dead(y)  cause(x,y,DeathByHeartAttack) [0.99]

●If someone triggers a loaded gun he is holding, and a bullet is off, he shot

● x:Man, y:Gun :

hold(x,y)  trigger(x,y)  loaded(y)  bullet_off(y)

 shoot(x)

●If a gun shoots, then it was loaded

● x:Gun : bullet_off(x)  loaded(x)

Common Sense Rules

●

Whoever shoots, he makes a dull, intense and sudden noise

●  x:Man : shoot(x)

  y : make_noise(x,y)  dull(y)  intense(y)  sudden(y)

●

Whoever makes an intense and sudden noise, he frightens emotional persons

●  x:Man, y:Man :  z  make_noise(x,z)

 intense(z)  sudden(z)  emotional(y)

 frighten(x,y) [0.9]

●

Whoever breaths, he leaves a halo on a mirror

●  x:Man : breath(x)  leave_halo(x,mirror)

(3)

Background Knowledge

●

Irrelevant Information

●Color of Objects

–color/2

●Nationality of people

–italian/1, french/1, english/1, ...

●

Constraints

●Either one triggers a gun, or he carries a cumbersome object, but not both

–trigger(x,Gun) XOR carry(x,CumbersomeObject) [0.97]

●It is not possible for one to hold something if he is carrying a cumbersome object

–hold(x,y) NAND carry(x,CumbersomeObject) [0.99]

Ontology

●

Example

Death

DiseaseDeath NaturalDeath ViolentDeath

DeathBy

HeartAttack DeathByGun DeathBy

ColdSteel ... ...

Gun

Rifle ...

Pistol is_a is_a

is_a is_a

is_a is_a is_a

is_a is_a

cause Animal

Man is_a

LivingBeing is_a

max peter

DeathBy Infection

subject_to

instance_of ... instance_of

Colt 1911

Beretta 92

is_a

is_a ...

oggetto847

instance_of ...

Abstraction

●

Irrelevant Information

●

color/2, italian/1

●

Facts

●

hold(peter,object847) s_n(object847,1234)

●

color(object847,black) bullet_off(object847)?

●

fearful(max) [0.98] italian(max)

●

has_heart_attack(max) still(max)

●

prone(max) leave_halo(max,mirror)

Argumentation

●

bullet_off(object847)?

It was in the morning

Jim heard object847 shooting

Jim is deaf

Jim wears a hearing aid

That day Jim forgot to wear it Jim always wears

it on holidays, and it was holiday

That day it was not holiday

In that moment there were fireworks

Argumentation

●

bullet_off(object847)?

●

P = 0.97

It was in the morning

Jim heard object847 shooting

Jim is deaf

Jim wears a hearing aid

That day Jim Jim always wears

it on holidays, and it was holiday

That day it was not holiday

In that moment there were fireworks

Deduction

●

Facts

–

bullet_off(object847) [0.97]

●

Deduction (Ontological)

Gun

Pistol is_a Beretta 92

is_a object847

instance_of

(4)

Deduction

●

Facts

–

bullet_off(object847) [0.97]

●

Deduction (Ontological)

–

object847:Gun

Gun

is_a object847

instance_of

Deduction

●

Facts

–

bullet_off(object847) [0.97]

●

Deduction (Ontological)

–

object847:Gun

●

Rule

–

 x:Gun : bullet_off(x)  loaded(x)

Gun

is_a object847

instance_of

Deduction

●

Facts

–

bullet_off(object847) [0.97]

●

Deduction (Ontological)

–

object847:Gun

●

Rule

–

 x:Gun : bullet_off(x)  loaded(x)

Gun

is_a object847

instance_of

Deduction

●

Facts

–

bullet_off(object847) [0.97]

●

Deduction (Ontological)

–

object847:Gun

●

Rule

–

 x:Gun : bullet_off(x)  loaded(x)

Gun

is_a object847

instance_of

Deduction

●

Facts

–

bullet_off(object847)

●

Deduction (Ontological)

–

object847:Gun

●

Rule

–

 x:Gun : bullet_off(x)  loaded(x)

●

Deduction (Modus Ponens)

–

loaded(object847) [0.97 x 1.0 = 0.97]

Gun

is_a object847

instance_of

Deduction

●

Facts

●

hold(peter,object847) bullet_off(object847) [0.97]

loaded(object847) object847:Gun

●

Deduction (Ontological)

●

peter:Man

●

Rule

●

 x:Man, y:Gun :

hold(x,y)  trigger(x,y)  loaded(y)  bullet_off(y)

 shoot(x)

● trigger(peter,object847)?

Man

peter instance_of

(5)

Abduction

●

Facts

●hold(peter,object847) object847:Gun

●

Constraints

●trigger(x,Gun) XOR carry(x,CumbersomeObject) [0.97]

●hold(x,y) NAND carry(x,CumbersomeObject) [0.99]

●

trigger(peter,object847)?

●

Abduction

●

Facts

●hold(peter,oggetto847) object847:Gun

●

Constraints

●

trigger(peter,object847)?

●

Abduction

●

Facts

●

Constraints

●

trigger(peter,object847)?

● carry(peter,CumbersomeObject) [0.99]

●

Abduction

●

Facts

●

Constraints

●

trigger(peter,object847)?

●

Abduction

●

Facts

●

Constraints

●

trigger(peter,object847)?

● trigger(peter,Gun) [0.97 x 0.99 = 0.96]

●

Abduction

●

Facts

●hold(peter,object847) object847:Gun

●

Constraints

●

trigger(peter,object847)?

●trigger(peter,Gun) [0.97 x 0.99 = 0.96]

●trigger(peter,object847) [0.96]

(6)

Deduction

●

Facts

●

peter:Man object847:Gun

impugna(peter,object847) bullet_off(object847) [0.97]

loaded(object847) trigger(peter,object847) [0.96]

●

Rule

●

 x:Man, y:Gun :

hold(x,y)  trigger(x,y)  loaded(y)  bullet_off(y)

 shoot(x)

●

Deduction (Modus Ponens)

●

shoot(peter) [min(0.96,0.97) x 1.0 = 0.96 x 1.0 = 0.96]

Deduction

●Facts

–peter:Man shoot(peter) [0.96]

●Rule

– x:Man : shoot(x)

●Deduzione (Modus Ponens)

–make_noise(peter,r32) [0.96] dull(r32) [0.96] intense(r32) [0.96] sudden(r32) [0.96]

● .

–.

● .

–. . –.

.

Deduction

●Facts

●Rule

●Deduction (ontological)

–Max:Man

● .

–. . –.

.

Man

max instance_of

Deduction

●Facts

●Rule

●Deduction (ontological)

–Max:Man

●Rule

– x:Man, y:Man :  z  make_noise(x,z)  intense(z)  sudden(z)  emotional(y)

–emotional(max)?

Man

max instance_of

Analogy

●

Emotional:

● Animal that can be affected by an entity or event that causes a sensorial or emotional stimulus that it perceives

–emotional(x) 

●animal(x)

●perceives(x,y)

●can_be_affected_by(x,z)

●entity_or_event(z)

●causes(z,y)

●stimulus(y)

●sensorial_or_emotional(y)

●

Fearful:

●

Animal that is doubtful or fearful of a possible entity or event characterized by its being dangerous or unpleasant

–fearful(i) 

●animal(i)

●doubtful_or_fearful_of(i,j)

●entity_or_event(j)

●possible(j)

●characteristic(j,k)

●dangerous_or_unpleasant(k)

Analogy

●

emotional(x) 

●

animal(x)

●

perceives(x,y)

●

can_be_affected_by(x,z)

●

entity_or_event(z)

●

causes(z,y)

●

stimulus(y)

●

sensorial_or_emotional(y)

●

fearful(i) 

●

animal(i)

●

doubtful_or_fearful_of(i,j)

●

entity_or_event(j)

●

possibile(j)

●

characteristic(j,k)

●

dangerous_or_unpleasant(k)

●

(7)

Analogy

●

emotional(x) 

●

animal(x)

●

perceives(x,y)

●

can_be_affected_by(x,z)

●

entity_or_event(z)

●

causes(z,y)

●

stimulus(y)

●

sensorial_or_emotional(y)

●

fearful(i) 

●

animal(i)

●

doubtful_or_fearful_of(i,j)

●

entity_or_event(j)

●

possible(j)

●

characteristic(j,k)

●

dangerous_or_unpleasant(k)

●

Analogy

●

emotional(x) 

●

animal(x)

●

perceives(x,y)

●

can_be_affected_by(x,z)

●

entity_or_event(z)

●

causes(z,y)

●

stimulus(y)

●

sensorial_or_emotional(y)

●

fearful(i) 

●

animal(i)

●

doubtful_or_fearful_of(i,j)

●

entity_or_event(j)

●

possible(j)

●

characteristic(j,k)

●

dangerous_or_unpleasant(k)

●

Analogy

●

emotional(x) 

●

animal(x)

●

perceives(x,y)

●

can_be_affected_by(x,z)

●

entity_or_event(z)

●

causes(z,y)

●

stimulus(y)

●

sensorial_or_emotional(y)

●

possible(z)

●

fearful(i) 

●

animal(i)

●

doubtful_or_fearful_of(i,j)

●

entity_or_event(j)

●

possible(j)

●

characteristic(j,k)

●

dangerous_or_unpleasant(k)

●

stimulus(i)

●

perceives(i,k)

emotional(x)  fearful(i) [0.94]

Deduction

●

Analogy

–fearful(max) [0.98] emotional(max) [0.98 x 0.94 = 0.92]

●

Facts

–peter:Man max:Man

–make_noise(peter,r32) [0.96] intense(r32) [0.96] sudden(r32) [0.96]

●

Rule

– x:Man, y:Man :

 z  make_noise(x,z)  intense(z)  sudden(z)  emotional(y)

●

Deduction (Modus Ponens)

–frighten(peter,max) [min(0.96,0.96,0.96,0.92) x 0.9 = 0.92 x 0.9 = 0.83]

Deduction

●

Facts

●

peter:Man max:Man

●

has_heart_attack(max) frighten(peter,max) [0.83]

●

Rule

●

 x:Man, y:Man :

frighten(x,y)  has_heart_attack(y)  dead(y)  cause(x,y,DeathByHeartAttack) [0.99]

●

dead(max)?

Induction

●Observations (about dead persons)

●Aristide is dead: he does not breath, he is supine, he has closed eyes and is still

–dead(Aristide) breath(Aristide) supine(Aristide) eyes(Aristide,closed) still(Aristide)

●Baldovino is dead: he does not breath, he is prone, and is still

–dead(Baldovino) breath(Baldovino) prone(Baldovino) still(Baldovino)

●Cesare is not dead: he breaths, he is not seated and he is still

–dead(Cesare) breath(Cesare) seated(Cesare) still(Cesare)

●Edgardo is dead: he does not breath, he is seated, he has open eyes and he is still

–dead(Edgardo) breath(Edgardo) seated(Edgardo) eyes(Edgardo,open) still(Edgardo)

●Davide is not dead: he does not breath, he is seated, he has open eyes and he is not still

–dead(Davide) breath(Davide) seated(Davide) eyes(Davide,open ) still(Davide)

●

● –

(8)

Induction

●Observations (about dead persons)

●Aristide is dead: he does not breath, he is supine, he has closed eyes and is still

–dead(Aristide) breath(Aristide) supine(Aristide) eyes(Aristide,closed) still(Aristide)

●Baldovino is dead: he does not breath, he is prone, and is still

–dead(Baldovino) breath(Baldovino) prone(Baldovino) still(Baldovino)

●Cesare is not dead: he breaths, he is not seated and he is still

–dead(Cesare) breath(Cesare) seated(Cesare) still(Cesare)

●Edgardo is dead: he does not breath, he is seated, he has open eyes and he is still

–dead(Edgardo) breath(Edgardo) seated(Edgardo) eyes(Edgardo,open) still(Edgardo)

●Davide is not dead: he does not breath, he is seated, he has open eyes and he is not still

–dead(Davide) breath(Davide) seated(Davide) eyes(Davide,open ) still(Davide)

● Rule

●Whoever does not breath and is still, he is dead

– x:Man : breath(x)  still(x)  dead(x) [0.92]

Deduction

●

Facts

●max:Man still(max) leave_halo(max,mirror)

●

Rule

● x:Man : breath(x)  still(x)  dead(x) [0.92]

●

breath(max)?

● –

●

Deduction

●

Facts

●

Rule

●

breath(max)?

● Rule

– x:Man : breath(x)  leave_halo(x,mirror)

● Deduction (Modus Tollens)

– breaths(max)

●

Deduction

●

Facts

●

Rule

●

breath(max)?

● Rule

– x:Man : breath(x)  leave_halo(x,mirror)

● Deduction (Modus Tollens)

– breaths(max)

●

Deduction (Modus Ponens)

● dead(max) [1.0 x 0.92 = 0.92]

Deduction

●

Facts

●

peter:Man max:Man has_heart_attack(max) dead(max) [0.92] frighten(peter,max) [0.83]

●

Rule

●

 x:Man, y:Man :

frighten(x,y)  has_heart_attack(y)  dead(y)

 cause(x,y,DeathByHeartAttack) [0.99]

●

Deduction (Modus Ponens)

●

cause(peter,max,DeathByHeartAttack) [min(0.92,0.83) x 0.99 = 0.83 x 0.99 = 0.82]

Deduction

●

Facts

●peter:Man max:Man cause(peter,max,DeatByHeartAttack) [0.82]

●

Rule

● x:Man, y:Man : cause(x,y,Death)  punishment(x,imprisonment,21,)

●cause(peter,max,Death)?

●DeathByHeartAttack is_a Death?

●

.

●.

(9)

Deduction

●

Facts

●peter:Man max:Man cause(peter,max,DeatByHeartAttack) [0.82]

●

Rule

● x:Man, y:Man : cause(x,y,Death)  punishment(x,imprisonment,21,)

●cause(peter,max,Death)?

●DeathByHeartAttack is_a Death?

●

Deduction (Ontological)

●DeathByHeartAttack:Death

●causes(peter,max,Death) [0.82]

Death

DeathByDisease

DeathBy HeartAttack

is_a

Deduction

●

Facts

●

peter:Man max:Man cause(peter,max,Death) [0.82]

●

Rule

●

 x:Man, y:Man : cause(x,y,Death)

 punishment(x,imprisonment,21,)

●

Deduction (Subsumption of the fact into the premises)

●