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Commonsense Reasoning 10/11 HC 11: Structured argumentation (3) / Dialogue Systems for Argumentation (1). Henry Prakken 12-01-2011. Overview. Structured argumentation Odd defeat loops Floating conclusions Which logic is the right one? Probabilistic reasoning

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commonsense reasoning 10 11 hc 11 structured argumentation 3 dialogue systems for argumentation 1

Commonsense Reasoning 10/11HC 11: Structured argumentation (3) /Dialogue Systems for Argumentation (1)

Henry Prakken

12-01-2011

overview
Overview
  • Structured argumentation
    • Odd defeat loops
    • Floating conclusions
    • Which logic is the right one?
    • Probabilistic reasoning
  • Dialogue systems for argumentation
    • Inference vs. dialogue
    • Use of argumentation in MAS
    • General ideas
slide3

R: W says that p  p

A: Alice says that Bob is unreliable,

so Bob is unreliable

Exception: W is unreliable

B: Bob says that Carole is unreliable,

so Carole is unreliable

E

D

C: Carole says that Alice is unreliable,

so Alice is unreliable

D: Bob says that John was the killer,

so John was the killer

A

B

E: Eric says that John was not the killer,

so John was not the killer

C

slide4

R: W says that p  p

A: Alice says that Bob is unreliable,

so Bob is unreliable

Exception: W is unreliable

B: Bob says that Carole is unreliable,

so Carole is unreliable

E

D

C: Carole says that Fred is unreliable,

so Fred is unreliable

F: Fred says that Alice is unreliable,

so Alice is unreliable

A

B

D: Bob says that John was the killer,

so John was the killer

F

C

E: Eric says that John was not the killer,

so John was not the killer

slide5

R: W says that p  p

A: Alice says that Bob is unreliable,

so Bob is unreliable

Exception: W is unreliable

B: Bob says that Carole is unreliable,

so Carole is unreliable

E

D

C: Carole says that Fred is unreliable,

so Fred is unreliable

F: Fred says that Alice is unreliable,

so Alice is unreliable

A

B

D: Bob says that John was the killer,

so John was the killer

F

C

E: Eric says that John was not the killer,

so John was not the killer

slide6

1. An argument is In iff all arguments defeating it are Out.

2. An argument is Out iff it is defeated by an argument that is In.

E

D

E

D

A

B

A

B

C

F

C

slide7

1. An argument is In iff all arguments defeating it are Out.

2. An argument is Out iff it is defeated by an argument that is In.

E

D

E

D

A

B

A

B

C

F

C

slide8

1. An argument is In iff all arguments defeating it are Out.

2. An argument is Out iff it is defeated by an argument that is In.

3. An argument is justified if it is In in all labellings

E

D

E

D

E is justified

E is not justified

A

B

A

B

C

F

C

slide9

S defends A if all defeaters of A are defeated by a member of S

S is admissible if it is conflict-free and defends all its members

{A,C,E} is admissible …

E

D

A

B

F

C

slide10

S defends A if all defeaters of A are defeated by a member of S

S is admissible if it is conflict-free and defends all its members

{A,C,E} is admissible …

E

D

{B,D,F} is admissible …

A

B

F

C

slide11

S defends A if all defeaters of A are defeated by a member of S

S is admissible if it is conflict-free and defends all its members

{E} is admissible …

E

D

A

B

C

slide12

S defends A if all defeaters of A are defeated by a member of S

S is admissible if it is conflict-free and defends all its members

{E} is admissible …

E

D

but {B,D} is not …

A

B

C

slide13

S defends A if all defeaters of A are defeated by a member of S

S is admissible if it is conflict-free and defends all its members

{E} is admissible …

E

D

but {B,D} is not …

A

B

C

and {A,B,D} is not

validating logics with intuitions 1 the general case
Validating logics with intuitions (1): the general case
  • The problem: check that a logic adequately formalises a reasoning practice
  • A method: formalise examples, and check whether the logic satisfies one’s intuitions
  • But whose intuitions: of logicians, of `ordinary’ language users, …
  • And what if intuitions conflict
validating logics with intuitions 2 the defeasible case
Validating logics with intuitions (2): the defeasible case
  • A special problem: how to distinguish counterexamples from abnormal situations?
  • Hypothesis: many “counterexamples” are based on new information that invalidates a defeasible inference.
floating conclusions
Floating conclusions

d1: x was born in Netherlands  x is Dutch

d2: x has Chinese name  x is Chinese

d3: x is Dutch  x likes badminton

d4: x is Chinese  x likes badminton

k1: Mei-li was born in the Netherlands

k2: Mei-li has a Chinese name

slide17

is justified iff in all p.s.a. an argument with conclusion  is In

(but it does not have to be the same argument)

In grounded semantics  is defensible,

in preferred semantics  is justified

Mei li likes badminton

Mei li likes badminton

Mei li is Dutch

Mei li is Chinese

Mei li was born in The Netherlands

Mei li has a Chinese name

floating conclusions invalid
Floating conclusions: invalid?
  • People tend to live in the same cities as their spouses
  • People tend to live in the city where they work
  • Carole works in A, her spouse works in B, so they live in A or B.

Horty’s counterexample: Carole works in A, her spouse John works in B, so they live in U (between A and B)

  • But isn’t this an exceptional situation?
which semantics is the right one
Which semantics is the “right” one?
  • Alternative semantics may each have their use in certain context
    • E.g. epistemic vs. practical reasoning
  • Dynamic aspects of reasoning makes this problem less urgent
floating conclusions still invalid horty
Floating conclusions:still invalid? (Horty)
  • Witness John says: the suspect shot the victim to death
  • If a witness says P then usually P is the case
  • So, the suspect shot the victim to death
  • So, the suspect killed the victim
  • Witness Bob says: the suspect stabbed the victim to death
  • If a witness says P then usually P is the case
  • So, the suspect stabbed the victim to death
  • So, the suspect killed the victim

One solution: add an undercutter “if two witnesses contradict each other, then they are both unreliable”

floating conclusions don t ignore dynamics
Floating conclusions:Don’t ignore dynamics
  • Any judge would ask further questions
    • Did you hear anything?
    • Where did you stand?
    • How dark was it?
  • The law’s way of dealing with dynamics:
    • Procedures for fair and effective dispute resolution
a simpler imaginary example
A simpler (imaginary) example
  • American civil law: evidence has to prove claim “on the balance of probabilities”
  • (Imaginary) statistic: 51% of American husbands commits adultery within 10 years.
  • Mary has been married to John for 10 years: can she sue John for divorce?
defeasibility and probability a paradox
Defeasibility and probability: a paradox
  • The lottery paradox:
    • A lottery with 1 million tickets and 1 prize.
    • The probability that some ticket wins is 1
    • The probability that a given ticket Li wins is 0.000001.
  • Is the conclusion that a given ticket will not win justified?
the lottery paradox in default logic
The lottery paradox in default logic
  • Problem: for no I is Li justified.
  • Solution HP: this is not a reasoning but a decision problem
why do agents need argumentation
Why do agents need argumentation?
  • For their internal reasoning
    • Reasoning about beliefs, goals, intentions etc often is defeasible
  • For their interaction with other agents
    • Information exchange involves explanation
    • Collaboration and negotiation involve conflict of opinion and persuasion
slide26

We should lower taxes

We should not lower taxes

Lower taxes increase productivity

Increased productivity is good

Lower taxes increase inequality

Increased inequality is bad

Increased inequality is good

Lower taxes do not increase productivity

Prof. P says that …

Prof. P is not objective

People with political ambitions are not objective

USA lowered taxes but productivity decreased

Increased inequality stimulates competition

Prof. P has political ambitions

Competition is good

slide27

claim

We should lower taxes

slide28

claim

why

We should lower taxes

slide29

claim

why

We should lower taxes

since

Lower taxes increase productivity

Increased productivity is good

slide30

claim

why

We should lower taxes

We should not lower taxes

since

since

Lower taxes increase productivity

Increased productivity is good

Lower taxes increase inequality

Increased inequality is bad

slide31

claim

why

We should lower taxes

We should not lower taxes

since

since

Lower taxes increase productivity

Increased productivity is good

Lower taxes increase inequality

Increased inequality is bad

claim

Increased inequality is good

slide32

claim

why

We should lower taxes

We should not lower taxes

since

since

Lower taxes increase productivity

Increased productivity is good

Lower taxes increase inequality

Increased inequality is bad

why

claim

Increased inequality is good

slide33

claim

why

We should lower taxes

We should not lower taxes

since

since

Lower taxes increase productivity

Increased productivity is good

Lower taxes increase inequality

Increased inequality is bad

why

claim

Increased inequality is good

since

Increased inequality stimulates competition

Competition is good

slide34

claim

why

We should lower taxes

We should not lower taxes

since

since

Lower taxes increase productivity

Increased productivity is good

Lower taxes increase inequality

Increased inequality is bad

claim

claim

Increased inequality is good

Lower taxes do not increase productivity

since

Increased inequality stimulates competition

Competition is good

slide35

claim

why

We should lower taxes

We should not lower taxes

since

since

Lower taxes increase productivity

Increased productivity is good

Lower taxes increase inequality

Increased inequality is bad

why

claim

claim

Lower taxes do not increase productivity

Increased inequality is good

since

Increased inequality stimulates competition

Competition is good

slide36

claim

why

We should lower taxes

We should not lower taxes

since

since

Lower taxes increase productivity

Increased productivity is good

Lower taxes increase inequality

Increased inequality is bad

why

claim

claim

Increased inequality is good

Lower taxes do not increase productivity

since

since

USA lowered taxes but productivity decreased

Increased inequality stimulates competition

Competition is good

slide37

claim

why

We should lower taxes

We should not lower taxes

since

since

why

Lower taxes increase productivity

Increased productivity is good

Lower taxes increase inequality

Increased inequality is bad

why

claim

claim

Increased inequality is good

Lower taxes do not increase productivity

since

since

USA lowered taxes but productivity decreased

Increased inequality stimulates competition

Competition is good

slide38

claim

why

We should lower taxes

We should not lower taxes

since

since

why

Lower taxes increase productivity

Increased productivity is good

Lower taxes increase inequality

Increased inequality is bad

since

why

claim

claim

Increased inequality is good

Lower taxes do not increase productivity

Prof. P says that …

since

since

USA lowered taxes but productivity decreased

Increased inequality stimulates competition

Competition is good

slide39

claim

why

We should lower taxes

We should not lower taxes

since

since

why

Lower taxes increase productivity

Increased productivity is good

Lower taxes increase inequality

Increased inequality is bad

since

why

claim

claim

Increased inequality is good

Lower taxes do not increase productivity

Prof. P says that …

Prof. P is not objective

since

since

since

People with political ambitions are not objective

USA lowered taxes but productivity decreased

Increased inequality stimulates competition

Prof. P has political ambitions

Competition is good

slide40

claim

why

We should lower taxes

We should not lower taxes

retract

since

since

why

Lower taxes increase productivity

Increased productivity is good

Lower taxes increase inequality

Increased inequality is bad

since

why

claim

claim

Increased inequality is good

Lower taxes do not increase productivity

Prof. P says that …

Prof. P is not objective

since

since

since

People with political ambitions are not objective

USA lowered taxes but productivity decreased

Increased inequality stimulates competition

Prof. P has political ambitions

Competition is good

types of dialogues walton krabbe

Dialogue Type

Dialogue Goal

Initial situation

Persuasion

resolution of conflict

conflict of opinion

Negotiation

making a deal

conflict of interest

Deliberation

reaching a decision

need for action

Information seeking

exchange of information

personal ignorance

Inquiry

growth of knowledge

general ignorance

Types of dialogues (Walton & Krabbe)
example
P: I offer you this Peugeot for $10000.

P: why do you reject my offer?

P: why are French cars no good?

P: why are French cars unsafe?

P: Meinwagen is biased since German car magazines usually are biased against French cars

P: why does Meinwagen have a very high reputation?.

P: OK, I accept your offer.

O: I reject your offer

O: since French cars are no good

O: since French cars are unsafe

O: since magazine Meinwagen says so

O: I concede that German car magazines usually are biased against French cars, butMeinwagen is not since it has a very high reputation.

O: OK, I retract that French cars are no good. Still I cannot pay $10.000; I offer $8.000.

Example
example 2
P: I offer you this Peugeot for $10000.

P: why do you reject my offer?

P: why are French cars no good?

P: why are French cars unsafe?

P: Meinwagen is biased since German car magazines usually are biased against French cars

P: why does Meinwagen have a very high reputation?.

P: OK, I accept your offer.

O: I reject your offer

O: since French cars are no good

O: since French cars are unsafe

O: since magazine Meinwagen says so

O: I concede that German car magazines usually are biased against French cars, but Meinwagen is not since it has a very high reputation.

O: OK, I retract that French cars are no good. Still I cannot pay $10.000; I offer $8.000.

Example (2)
example 3
P: I offer you this Peugeot for $10000.

P: why do you reject my offer?

P: why are French cars no good?

P: why are French cars unsafe?

P: Meinwagen is biased since German car magazines usually are biased against French cars

P: why does Meinwagen have a very high reputation?.

P: OK, I accept your offer.

O: I reject your offer

O: since French cars are no good

O: since French cars are unsafe

O: since magazine Meinwagen says so

O: I concede that German car magazines usually are biased against French cars, but Meinwagen is not since it has a very high reputation.

O: OK, I retract that French cars are no good. Still I cannot pay $10.000; I offer $8.000.

Example (3)
inference vs dialogue
Inference vs dialogue
  • Dialogue systems for argumentation have:
    • A communication language (well-formed utterances)
    • A protocol (which utterances are allowed at which point?)
      • Termination and outcome rules
  • Argument games are a proof theory for a logic
  • But real argumentation dialogues have real players!
      • Distributed information
      • Richer communication languages
      • Dynamics
standards for argumentation formalisms
Standards for argumentation formalisms
  • Logical argument games: soundness and completeness wrt some semantics of an argumentation logic
  • Dialogue systems: effectiveness wrt dialogue goal and fairness wrt participants’ goals
    • Argumentation:
      • Dialogue goal = rational resolution of conflicts of opinion
      • Participants’ goal = to persuade
some properties of dialogue systems that can be studied
Some properties of dialogue systems that can be studied
  • Correspondence of outcome with players’ beliefs
    • If the union of participants’ beliefs justifies p, can/will agreement on p result?
    • If participants’ agree on p, does the union of their beliefs justify p?
    • Disregarding vs. assuming participants’ personalities
game for grounded semantics unsound in distributed settings
Game for grounded semantics unsound in distributed settings

Knowledge bases

Inference rules

p  q

s q

r s

r p

Paul: p, r

P1: q since p

Olga: s

game for grounded semantics unsound in distributed settings49
Game for grounded semantics unsound in distributed settings

Knowledge bases

Inference rules

p  q

s q

r s

r p

Paul: p, r

P1: q since p

Olga: s

O1: q since s

game for grounded semantics unsound in distributed settings50
Game for grounded semantics unsound in distributed settings

Knowledge bases

Inference rules

p  q

s q

r s

r p

Paul: p, r

P1: q since p

Olga: s, r

O1: q since s

P2: s since r

game for grounded semantics unsound in distributed settings51
Game for grounded semantics unsound in distributed settings

Knowledge bases

Inference rules

p  q

s q

r s

r p

Paul: p, r

P1: q since p

Olga: s, r

O1: q since s

P2: s since r

O2: p since r

example 1
Example 1

Knowledge bases

Inference rules

p  q

r p

s r

Paul: r

P1: q since p

Olga: s

Olga is credulous: she concedes everything for which she cannot construct a (defensible or justified) counterargument

Paul  Olga does not justify q but they could agree on q

example 153
Example 1

Knowledge bases

Inference rules

p  q

r p

s r

Paul: r

P1: q since p

Olga: s

O1: concede p,q

Paul  Olga does not justify q but they could agree on q

example 154
Example 1

Knowledge bases

Inference rules

p  q

r p

s r

Paul: r

P1: q since p

Olga: s

Paul  Olga does not justify q but they could agree on q

Olga is sceptical: she challenges everything for which she cannot construct a (defensible or justified) argument

example 155
Example 1

Knowledge bases

Inference rules

p  q

r p

s r

Paul: r

P1: q since p

Olga: s

O1: why p?

Paul  Olga does not justify q but they could agree on q

example 156
Example 1

Knowledge bases

Inference rules

p  q

r p

s r

Paul: r

P1: q since p

Olga: s

O1: why p?

P2: p since r

Paul  Olga does not justify q but they could agree on q

example 157
Example 1

Knowledge bases

Inference rules

p  q

r p

s r

Paul: r

P1: q since p

Olga: s

O1: why p?

P2: p since r

Paul  Olga does not justify q but they could agree on q

O2: r since s

example 258
Example 2

Knowledge bases

Inference rules

Modus ponens

Paul:

p

q

P1: claim p

Olga:

p

q  p

Paul  Olga does not justify p but they will agree on p if players are conservative, that is, if they stick to their beliefs if possible

example 259
Example 2

Knowledge bases

Inference rules

Modus ponens

Paul:

p

q

P1: claim p

O1: concede p

Olga:

p

q  p

Paul  Olga does not justify p but they will agree on p if players are conservative, that is, if they stick to their beliefs if possible

example 260
Example 2

Knowledge bases

Inference rules

Modus ponens

Paul:

p

q

P1: claim p

O1: what about q?

Olga:

p

q  p

Possible solution (for open-minded agents, who are prepared to critically test their beliefs):

example 261
Example 2

Knowledge bases

Inference rules

Modus ponens

Paul:

p

q

P1: claim p

O1: what about q?

Olga:

p

q  p

P2: claim q

Possible solution (for open-minded agents, who are prepared to critically test their beliefs):

example 262
Example 2

Knowledge bases

Inference rules

Modus ponens

Paul:

p

q

P1: claim p

O1: what about q?

Olga:

p

q  p

Problem: how to

ensure relevance?

P2: claim q

O2: p since q, q  p

Possible solution (for open-minded agents, who are prepared to critically test their beliefs):

dialogue game systems in more detail
Dialogue game systems in more detail
  • A dialogue purpose
  • Participants (with roles)
  • A topic language Lt
    • With a logic
  • A communication language Lc
    • With a protocol
      • Move legality rules
      • Effect rules for Lc (“commitment rules”)
      • Turntaking rules
      • Termination and outcome rules
effect rules
Effect rules
  • Specify commitments
    • “Claim p” and “Concede p” commits to p
    • “p since Q” commits to p and Q
    • “Retract p” ends commitment to p
    • ...
  • Commitments used for:
    • Determining outcome
    • Enforcing ‘dialogical consistency’
    • ...
public semantics for dialogue protocols
Public semantics for dialogue protocols
  • Public semantics: can protocol compliance be externally observed?
  • Commitments are a participant’s publicly declared standpoints, so not the same as beliefs!
  • Only commitments and dialogical behaviour should count for move legality:
    • “Claim p is allowed only if you believe p”

vs.

    • “Claim p is allowed only if you are not committed to p and have not challenged p”
more and less strict protocols
More and less strict protocols
  • Single-multi move: one or more moves per turn allowed
  • Single-multi-reply: one or more replies to the same move allowed
  • Deterministic: no choice from legal moves
  • Deterministic in Lc: no choice from speech act types
  • Only reply to moves from previous turn?