Argumentation

1
Argumentation

• Henry Prakken
• SIKS Basic Course
• Learning and Reasoning
• May 26th, 2009

2
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, negotiation, collaboration,
  

3
Overview

• Inference (logic)
• Abstract argumentation
• Rule-based argumentation
• Dialogue

4
Part 1Inference
5
We should lower taxes
Lower taxes increase productivity
Increased productivity is good
6
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
7
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
Lower taxes do not increase productivity
USA lowered taxes but productivity decreased
8
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
Lower taxes do not increase productivity
Prof. P says that
USA lowered taxes but productivity decreased
9
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
Lower taxes do not increase productivity
Prof. P says that
Prof. P is not objective
Prof. P has political ambitions
People with political ambitions are not objective
USA lowered taxes but productivity decreased
10
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
Lower taxes do not increase productivity
Prof. P says that
Prof. P is not objective
Prof. P has political ambitions
People with political ambitions are not objective
USA lowered taxes but productivity decreased
11
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
Lower taxes do not increase productivity
Increased inequality is good
Prof. P says that
Prof. P is not objective
Prof. P has political ambitions
People with political ambitions are not objective
Increased inequality stimulates competition
USA lowered taxes but productivity decreased
Competition is good
12
Sources of conflict

• Default generalisations
• Conflicting information sources
• Alternative explanations
• Conflicting goals, interests
• Conflicting normative, moral opinions

13
Application areas

• Medical diagnosis and treatment
• Legal reasoning
• Interpretation
• Evidence / crime investigation
• Intelligence
• Decision making
• Policy design

14
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
Lower taxes do not increase productivity
Increased inequality is good
Prof. P says that
Prof. P is not objective
Prof. P has political ambitions
People with political ambitions are not objective
Increased inequality stimulates competition
USA lowered taxes but productivity decreased
Competition is good
15
A
B
E
D
C
16
Status of arguments abstract semantics (Dung
1995)

• INPUT a pair ?Args,Defeat?
• OUTPUT An assignment of the status in or out
  to all members of Args
• So semantics specifies conditions for labeling
  the argument graph.
• Should capture reinstatement

A
B
C
17
Possible labeling conditions

• Every argument is either in or out.
• 1. An argument is in if all arguments defeating
  it are out.
• 2. An argument is out if it is defeated by an
  argument that is in.
• Works fine with
• But not with

A
B
C
A
B
18
Two solutions

• Change conditions so that always a unique status
  assignment results
• Use multiple status assignments
• and

A
B
C
A
B
A
B
C
A
B
A
B
19
Unique status assignments

• Grounded semantics (Dung 1995)
• S0 the empty set
• Si1 Si all arguments defended by Si
• ...
• (S defends A if all defeaters of A are defeated
  by a member of S)

20
A
B
E
D
C
Is B or E defended by S2?
Is B, D or E defended by S1?
21
A problem(?) with grounded semantics

• We have We want(?)

A
B
A
B
C
C
D
D
22
A problem(?) with grounded semantics

A
B
C
A Frederic Michaud is French since he has a
French name B Frederic Michaud is Dutch since
he is a marathon skater C F.M. likes the EU
since he is European (assuming he is not
Dutch or French) D F.M. does not like the EU
since he looks like a person who does not
like the EU
D
23
A problem(?) with grounded semantics
E

A
B
C
A Frederic Michaud is French since Alice says
so B Frederic Michaud is Dutch since Bob says
so C F.M. likes the EU since he is European
(assuming he is not Dutch or French) D
F.M. does not like the EU since he looks like a
person who does not like the EU
D
E Alice and Bob are unreliable since they
contradict each other
24
Multiple labellings
A
B
A
B
C
C
D
D
25
Status assignments (1)

• Given ?Args,Defeat?
• A status assignment is a partition of Args into
  sets In and Out such that
• 1. An argument is in In if all arguments
  defeating it are in Out.
• 2. An argument is in Out if it is defeated by an
  argument that is in In.

26
Status assignments (1)

• Given ?Args,Defeat?
• A status assignment is a partition of Args into
  sets In and Out such that
• 1. An argument is in In if all arguments
  defeating it are in Out.
• 2. An argument is in Out if it is defeated by an
  argument that is in In.

A
B
C
27
Status assignments (1)

• Given ?Args,Defeat?
• A status assignment is a partition of Args into
  sets In and Out such that
• 1. An argument is in In if all arguments
  defeating it are in Out.
• 2. An argument is in Out if it is defeated by an
  argument that is in In.

A
B
C
28
Status assignments (1)

• Given ?Args,Defeat?
• A status assignment is a partition of Args into
  sets In and Out such that
• 1. An argument is in In if all arguments
  defeating it are in Out.
• 2. An argument is in Out if it is defeated by an
  argument that is in In.

A
B
C
29
Status assignments (1)

• Given ?Args,Defeat?
• A status assignment is a partition of Args into
  sets In and Out such that
• 1. An argument is in In if all arguments
  defeating it are in Out.
• 2. An argument is in Out if it is defeated by an
  argument that is in In.

A
B
C
30
Status assignments (2)

• Given ?Args,Defeat?
• A status assignment is a partition of Args into
  sets In, Out and Undecided such that
• 1. An argument is in In if all arguments
  defeating it are in Out.
• 2. An argument is in Out if it is defeated by an
  argument that is in In.
• A status assignment is stable if Undecided ?.
• In is a stable extension
• A status assignment is preferred if Undecided is
  ?-minimal.
• In is a preferred extension
• A status assignment is grounded if Undecided is
  ?-maximal.
• In is the grounded extension

31
Dungs original definitions

• Given ?Args,Defeat?, S ? Args, A ? Args
• S is conflict-free if no member of S defeats a
  member of S
• 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
• S is a preferred extension if it is ?-maximally
  admissible
• S is a stable extension if it is conflict-free
  and defeats all arguments outside it
• S is the grounded extension if S is the
  ?-smallest set such that A ? S iff S defends A.

32
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
B
E
D
C
Admissible?
33
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
B
E
D
C
Admissible?
34
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
B
E
D
C
Admissible?
35
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
B
E
D
C
Admissible?
36
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
B
E
D
C
S is preferred if it is maximally admissible
Preferred?
37
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
B
E
D
C
S is preferred if it is maximally admissible
Preferred?
38
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
B
E
D
C
S is preferred if it is maximally admissible
Preferred?
39
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
B
E
D
C
S is groundeded if it is the smallest set s.t. A
? S iff S defends A
Grounded?
40
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
B
E
D
C
S is groundeded if it is the smallest set s.t. A
? S iff S defends A
Grounded?
41
Properties

• The grounded extension is unique
• Every stable extension is preferred (but not
  v.v.)
• There exists at least one preferred extension
• The grounded extension is a subset of all
  preferred and stable extensions

42
The ultimate status of arguments (and
conclusions)

• With grounded semantics
• A is justified if A ? g.e.
• A is overruled if A ? g.e. and A is defeated by
  g.e.
• A is defensible otherwise
• With preferred semantics
• A is justified if A ? p.e for all p.e.
• A is defensible if A ? p.e. for some but not all
  p.e.
• A is overruled otherwise (?)
• In all semantics
• ? is justified if ? is the conclusion of some
  justified argument
• ? is defensible if ? is not justified and ? is
  the conclusion of some defensible argument

43
The status of arguments proof theory

• Argument games between proponent and opponent
• Proponent starts with an argument
• Then each party replies with a suitable
  counterargument
• Possibly backtracking
• A winning criterion
• E.g. the other player cannot move
• An argument is (dialectically) provable iff
  proponent has a winning strategy in a game for
  it.

44
The G-game for grounded semantics

• A sound and complete game
• Each move replies to previous move
• Proponent does not repeat moves
• Proponent moves strict defeaters, opponent moves
  defeaters
• A player wins iff the other player cannot move
• Result A is in the grounded extension iff
  proponent has a winning strategy in a game about
  A.

45
A game tree
A
F
B
C
E
D
46
A game tree
P A
A
F
B
C
E
D
47
A game tree
P A
A
F
O F
B
C
E
D
48
A game tree
P A
A
F
O F
B
P E
C
E
D
49
A game tree
P A
A
F
O B
O F
B
P E
C
E
D
50
A game tree
P A
A
F
O B
O F
B
P C
P E
C
E
D
51
A game tree
P A
A
F
O B
O F
B
P C
P E
C
E
O D
D
52
A game tree
P A
A
F
O B
O F
B
P C
P E
P E
C
E
O D
D
53
The structure of arguments current accounts

• Assumption-based approaches (Dung-Kowalski-Toni,
  Besnard Hunter, )
• K theory
• A assumptions, - is conflict relation on A
• R inference rules (strict)
• An argument for p is a set A ? A such that A ?
  K -R p
• Arguments attack each other on their assumptions
• Rule-based approaches (Pollock, Vreeswijk, DeLP,
  Prakken Sartor, Defeasible Logic, )
• K theory
• R inference rules (strict and defeasible)
• K yields an argument for p if K -R p
• Arguments attack each other on applications of
  defeasible inference rules

54
Aspic system overview

• Argument structure based on Vreeswijk (1997)
• Trees where
• Nodes are wff of logical language L closed under
  negation
• Links are applications of inference rules
• Strict (?1, ..., ?1 ? ?) or
• Defeasible (?1, ..., ?1 ? ?)
• Reasoning starts from knowledge base K ? L
• Defeat based on Pollock
• Argument acceptability based on Dung (1995)

55
ASPIC system structure of arguments

• An argument A is
• ? if ? ? K with
• Conc(A) ?
• Sub(A) ?
• A1, ..., An ? ? if there is a strict inference
  rule Conc(A1), ..., Conc(An) ? ?
• Conc(A) ?
• Sub(A) Sub(A1) ? ... ? Sub(An) ? A
• A1, ..., An ? ? if there is a defeasible
  inference rule Conc(A1), ..., Conc(An) ? ?
• Conc(A) ?
• Sub(A) Sub(A1) ? ... ? Sub(An) ? A
• A is strict if all members of Sub(A) apply strict
  rules else A is defeasible

56
Q1, Q2 ? P
Q1,R1,R2 ? K
R1, R2 ? Q2
57
Domain-specific vs. inference general inference
rules

• R1 Bird ? Flies
• R2 Penguin ? Bird
• Penguin ? K
• R1 ?, ? ? ? ? ?
• Strict rules all deductively
• valid inference rules
• Bird ? Flies ? K
• Penguin ? Bird ? K
• Penguin ? K

58
ASPIC system attack and defeat

• is a preference ordering between arguments such
  that if A is strict and B is defeasible then A gt
  B
• A rebuts B if
• Conc(A) Conc(B ) for some B ? Sub(B) and
• B applies a defeasible rule and
• not B gt A
• A undercuts B if
• Conc(A) B for some B ? Sub(B) and
• B applies a defeasible rule
• A defeats B if A rebuts or undercuts B

Naming convention implicit
59
(No Transcript)
60
Argument acceptability

• Dung-style semantics and proof theory directly
  apply!

61
Additional properties(cf. Caminada Amgoud 2007)

• Let E be any stable, preferred or grounded
  extension
• If B ? Sub(A) and A ? E then B ? E
• If the strict rules RS are closed under
  contraposition, then ?? Conc(A) for some A ?
  E is
• closed under RS
• consistent if K is consistent

62
Argument schemes

• Many arguments (and attacks) follow patterns.
• Much work in argumentation theory (Perelman,
  Toulmin, Walton, ...)
• Argument schemes
• Critical questions
• Recent applications in AI ( Law)

63
Argument schemes general form

• But also critical questions
• Negative answers are counterarguments

Premise 1, , Premise n Therefore
(presumably), conclusion
64
Expert testimony(Walton 1996)

• Critical questions
• Is E biased?
• Is P consistent with what other experts say?
• Is P consistent with known evidence?

E is expert on D E says that P P is within D
Therefore (presumably),
P is the case
65
Witness testimony

• Critical questions
• Is W sincere? (veracity)
• Was P evidenced by Ws senses? (objectivity)
• Did P occur? (observational sensitivity)

Witness W says P Therefore (presumably), P
66
Perception

• Critical questions
• Are the circumstances such that reliable
  observation of P is impossible?

P is observed Therefore (presumably), P
67
Memory

• Critical questions
• Was P originally based on beliefs of which one is
  false?

P is recalled Therefore (presumably), P
68
Unpacking the witness testimony scheme
Witness testimony

• Critical questions
• Is W sincere? (veracity)
• Was P evidenced by Ws senses? (objectivity)
• Did P occur? (observational sensitivity)

Witness W says I remember I saw P Therefore
(presumably), W remembers he saw P Therefore
(presumably), W saw P Therefore (presumably), P
Witness testimony
69
Unpacking the witness testimony scheme

• Critical questions
• Is W sincere? (veracity)
• Was P evidenced by Ws senses? (objectivity)
• Did P occur? (observational sensitivity)

Witness W says I remember I saw P Therefore
(presumably), W remembers he saw P Therefore
(presumably), W saw P Therefore (presumably), P
Memory
Memory
70
Unpacking the witness testimony scheme

• Critical questions
• Is W sincere? (veracity)
• Was P evidenced by Ws senses? (objectivity)
• Did P occur? (observational sensitivity)

Witness W says I remember I saw P Therefore
(presumably), W remembers he saw P Therefore
(presumably), W saw P Therefore (presumably), P
Perception
Perception
71
Applying commonsense generalisations
Consc of Guilt

• Critical questions are there exceptions to the
  generalisation?
• exceptional classes of people may have other
  reasons to flea
• Illegal immigrants
• Customers of prostitutes

P If P then usually Q Therefore (presumably), Q
If Fleas then usually Consc of Guilt
Fleas
People who flea from a crime scene usually have
consciousness of guilt
72
Arguments from consequences

• Critical questions
• Does A also have bad (good) consequences?
• Are there other ways to bring about G?
• ...

Action A brings about G, G is good
(bad) Therefore (presumably), A should (not) be
done
73
Other work on argument-based inference

• Reasoning about priorities and defeat
• Abstract support relations between arguments
• Gradual defeat
• Other semantics
• Dialectical proof theories
• Combining modes of reasoning
• ...

74
Part 2Dialogue
75
Argument is ambiguous

• Inferential structure
• Single agents
• (Nonmonotonic) logic
• Fixed information state
• Form of dialogue
• Multiple agents
• Dialogue theory
• Changing information state

76
Example

• P Tell me all you know about recent trading in
  explosive materials (request)
• P why dont you want to tell me?
• P why arent you allowed to tell me?
• P You may be right in general (concede) but in
  this case there is an exception since this is a
  matter of national importance
• P since we have heard about a possible terrorist
  attack
• P OK, I agree (offer accepted).

• O No I wont (reject)
• O since I am not allowed to tell you
• O since sharing such information could endanger
  an investigation
• O Why is this a matter of national importance?
• O I concede that there is an exception, so I
  retract that I am not allowed to tell you. I will
  tell you on the condition that you dont exchange
  the information with other police officers (offer)

77
Example

• P Tell me all you know about recent trading in
  explosive materials (request)
• P why dont you want to tell me?
• P why arent you allowed to tell me?
• P You may be right in general (concede) but in
  this case there is an exception since this is a
  matter of national importance
• P since we have heard about a possible terrorist
  attack
• P OK, I agree (offer accepted).

• O No I wont (reject)
• O since I am not allowed to tell you
• O since sharing such information could endanger
  an investigation
• O Why is this a matter of national importance?
• O I concede that there is an exception, so I
  retract that I am not allowed to tell you. I will
  tell you on the condition that you dont exchange
  the information with other police officers (offer)

78
Example

• P Tell me all you know about recent trading in
  explosive materials (request)
• P why dont you want to tell me?
• P why arent you allowed to tell me?
• P You may be right in general (concede) but in
  this case there is an exception since this is a
  matter of national importance
• P since we have heard about a possible terrorist
  attack
• P OK, I agree (offer accepted).

• O No I wont (reject)
• O since I am not allowed to tell you
• O since sharing such information could endanger
  an investigation
• O Why is this a matter of national importance?
• O I concede that there is an exception, so I
  retract that I am not allowed to tell you. I will
  tell you on the condition that you dont exchange
  the information with other police officers (offer)

79
Types of dialogues (Walton Krabbe)
80
Dialogue systems (according to Carlson 1983)

• Dialogue systems define the conditions under
  which an utterance is appropriate
• An utterance is appropriate if it promotes the
  goal of the dialogue in which it is made
• Appropriateness defined not at speech act level
  but at dialogue level
• Dialogue game approach
• Protocol should promote the goal of the dialogue

81
Formal dialogue systems

• Topic language
• With a logic (possibly nonmonotonic)
• Communication language
• Locution content (from topic language)
• With a protocol rules for when utterances may be
  made
• Should promote the goal of the dialogue
• Effect rules (e.g. on agents commitments)
• Termination and outcome rules

82
Negotiation

• Dialogue goal making a deal
• Participants goals maximise individual gain
• Typical communication language
• Request p, Offer p, Accept p, Reject p,

83
Persuasion

• Participants proponent (P) and opponent (O) of a
  dialogue topic T
• Dialogue goal resolve the conflict of opinion on
  T
• Participants goals
• P wants O to accept T
• O wants P to give up T
• Typical speech acts
• Claim p, Concede p, Why p, p since S, Retract p,
  Deny p

Goal of argument games Verify logical status of
argument or proposition relative to given theory
84
Standards for dialogue systems

• Argument games soundness and completeness wrt
  some logical semantics
• Dialogue systems
• Effectiveness wrt dialogue goal
• Efficiency, relevance, termination, ...
• Fairness wrt participants goals
• Can everything relevant be said?, ...

85
Some standards for persuasion systems

• Correspondence
• With participants beliefs
• If union of beliefs implies p, can/will agreement
  on p result?
• If parties agree that p, does the union of their
  beliefs imply p?
• ...
• With dialogue theory
• If union of commitments implies p, can/will
  agreement on p result?
• ...

86
A communication language (Dijkstra et al. 2007)
Speech act Attack Surrender
request(?) offer (?), reject(?) -
offer(?) offer(?) (? ? ?), reject(?) accept(?)
reject(?) offer(?) (? ? ?), why-reject (?) -
accept(?) - -
why-reject(?) claim (?) -
claim(?) why(?) concede(?)
why(?) ? since S (an argument) retract(?)
? since S why(?) (? ? S) ? since S (a defeater) concede(?) concede ? (? ? S)
concede(?) - -
retract(?) - -
deny(?) - -
87
A protocol (Dijkstra et al. 2007)

• Start with a request
• Repy to a previous move of the other agent
• Pick your replies from the table
• Finish persuasion before resuming negotiation
• Turntaking
• In nego after each move
• In pers various rules possible
• Termination
• In nego if offer is accepted or someone
  withdraws
• In pers if main claim is retracted or conceded

88
Example dialogue formalised
P Request to tell
O Reject to tell
P Why reject to tell?
Embedded persuasion ...
O Offer to tell if no further exchange
P Accept after tell no further exchange
89
Persuasion part formalised
O Claim Not allowed to tell
P Why not allowed to tell?
O Not allowed to tell since telling endangers
investigation What endangers an investigation
is not allowed
P Concede What endangers an investigation is
not allowed
P Exception to R1 since National importance
National importance ? Exception to R1
O Why National importance?
P National importance since Terrorist threat
Terrorist threat ? National importance
90
Persuasion part formalised
O Claim Not allowed to tell
P Why not allowed to tell?
O Not allowed to tell since telling endangers
investigation What endangers an investigation
is not allowed
P Concede What endangers an investigation is
not allowed
P Exception to R1 since National importance
National importance ? Exception to R1
O Why National importance?
P Concede Exception to R1
P National importance since Terrorist threat
Terrorist threat ? National importance
91
Persuasion part formalised
O Claim Not allowed to tell
P Why not allowed to tell?
O Retract Not allowed to tell
O Not allowed to tell since telling endangers
investigation What endangers an investigation
is not allowed
P Concede What endangers an investigation is
not allowed
P Exception to R1 since National importance
National importance ? Exception to R1
O Why National importance?
O Concede Exception to R1
P National importance since Terrorist threat
Terrorist threat ? National importance
92
Theory building in dialogue

• In my 2005 approach to (persuasion) dialogue
• Agents build a joint theory during the dialogue
• A dialectical graph
• Moves are operations on the joint theory

93
claim
Not allowed to tell
94
claim
why
Not allowed to tell
95
claim
why
Not allowed to tell
since
Telling endangers investigation
R1 What endangers an investigation is not allowed
96
claim
why
Not allowed to tell
since
concede
Telling endangers investigation
R1 What endangers an investigation is not allowed
97
claim
why
Not allowed to tell
since
concede
Telling endangers investigation
R1 What endangers an investigation is not allowed
Exception to R1
since
National importance
R2 national importance ? Not R1
98
claim
why
Not allowed to tell
since
concede
Telling endangers investigation
R1 What endangers an investigation is not allowed
Exception to R1
since
why
National importance
R2 national importance ? Not R1
99
claim
why
Not allowed to tell
since
concede
Telling endangers investigation
R1 What endangers an investigation is not allowed
Exception to R1
since
why
National importance
R2 national importance ? Not R1
since
Terrorist threat ? national importance
Terrorist threat
100
claim
why
Not allowed to tell
since
concede
Telling endangers investigation
R1 What endangers an investigation is not allowed
concede
Exception to R1
since
why
National importance
R2 national importance ? Not R1
since
Terrorist threat ? national importance
Terrorist threat
101
claim
why
Not allowed to tell
retract
since
concede
Telling endangers investigation
R1 What endangers an investigation is not allowed
concede
Exception to R1
since
why
National importance
R2 national importance ? Not R1
since
Terrorist threat ? national importance
Terrorist threat
102
Research issues

• Investigation of protocol properties
• Mathematical proof or experimentation
• Combinations of dialogue types
• Deliberation!
• Multi-party dialogues
• Dialogical agent behaviour (strategies)
• ...

103
Further information

• http//people.cs.uu.nl/henry/siks/siks09.html