Argumentation
Henry Prakken
SIKS Basic Course
Learning and Reasoning
May 26th, 2009
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, …
Overview

Inference (logic)



Abstract argumentation
Rule-based argumentation
Dialogue
Part 1:
Inference
We should lower taxes
Lower taxes
increase
productivity
Increased
productivity
is good
We should lower taxes
Lower taxes
increase
productivity
Increased
productivity
is good
We should not lower taxes
Lower taxes
increase
inequality
Increased
inequality
is bad
We should lower taxes
Lower taxes
increase
productivity
We should not lower taxes
Increased
productivity
is good
Lower taxes do
not increase
productivity
USA lowered
taxes but
productivity
decreased
Lower taxes
increase
inequality
Increased
inequality
is bad
We should lower taxes
Lower taxes
increase
productivity
Prof. P says
that …
We should not lower taxes
Increased
productivity
is good
Lower taxes do
not increase
productivity
USA lowered
taxes but
productivity
decreased
Lower taxes
increase
inequality
Increased
inequality
is bad
We should lower taxes
Lower taxes
increase
productivity
Prof. P says
that …
People with
political
ambitions
are not
objective
We should not lower taxes
Increased
productivity
is good
Prof. P is not
objective
Prof. P has
political
ambitions
Lower taxes do
not increase
productivity
USA lowered
taxes but
productivity
decreased
Lower taxes
increase
inequality
Increased
inequality
is bad
We should lower taxes
Lower taxes
increase
productivity
Prof. P says
that …
People with
political
ambitions
are not
objective
We should not lower taxes
Increased
productivity
is good
Prof. P is not
objective
Prof. P has
political
ambitions
Lower taxes do
not increase
productivity
USA lowered
taxes but
productivity
decreased
Lower taxes
increase
inequality
Increased
inequality
is bad
We should lower taxes
Lower taxes
increase
productivity
Prof. P says
that …
People with
political
ambitions
are not
objective
We should not lower taxes
Increased
productivity
is good
Prof. P is not
objective
Prof. P has
political
ambitions
Lower taxes
increase
inequality
Increased
inequality
is good
Lower taxes do
not increase
productivity
USA lowered
taxes but
productivity
decreased
Increased
inequality
is bad
Increased
inequality
stimulates
competition
Competition
is good
Sources of conflict






Default generalisations
Conflicting information sources
Alternative explanations
Conflicting goals, interests
Conflicting normative, moral opinions
…
Application areas


Medical diagnosis and treatment
Legal reasoning






Interpretation
Evidence / crime investigation
Intelligence
Decision making
Policy design
…
We should lower taxes
Lower taxes
increase
productivity
Prof. P says
that …
People with
political
ambitions
are not
objective
We should not lower taxes
Increased
productivity
is good
Prof. P is not
objective
Prof. P has
political
ambitions
Lower taxes
increase
inequality
Increased
inequality
is good
Lower taxes do
not increase
productivity
USA lowered
taxes but
productivity
decreased
Increased
inequality
is bad
Increased
inequality
stimulates
competition
Competition
is good
A
C
B
D
E
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
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:
A
B

But not with:
A
B
C
Two solutions

Change conditions so that always a unique status
assignment results
A
B
A

A
B
Use multiple status assignments:
A

C
B
B
and
C
A
B
Unique status assignments

Grounded semantics (Dung 1995):




S0: the empty set
Si+1: Si + all arguments defended by Si
...
(S defends A if all defeaters of A are
defeated by a member of S)
A
C
B
D
E
Is B, D or E defended by S1? Is B or E defended by S2?
A problem(?) with grounded
semantics
We have:
A
B
We want(?):
A
B
C
C
D
D
A problem(?) with grounded
semantics
A
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
B
C
D
A problem(?) with grounded
semantics
E
A
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
E = Alice and Bob are unreliable since they contradict each other
B
C
D
Multiple labellings
A
B
A
B
C
C
D
D
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
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
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
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
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
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 = .


A status assignment is preferred if Undecided is -minimal.


In is a stable extension
In is a preferred extension
A status assignment is grounded if Undecided is -maximal.

In is the grounded extension
Dung’s 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.
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
B
D
Admissible?
E
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
B
D
Admissible?
E
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
B
D
Admissible?
E
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
B
D
Admissible?
E
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
B
D
Preferred?
E
S is preferred if it is
maximally admissible
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
B
D
Preferred?
E
S is preferred if it is
maximally admissible
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
B
D
Preferred?
E
S is preferred if it is
maximally admissible
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
B
D
Grounded?
E
S is groundeded if it
is the smallest set s.t.
A  S iff S defends A
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
B
D
Grounded?
E
S is groundeded if it
is the smallest set s.t.
A  S iff S defends A
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
…
The ‘ultimate’ status of
arguments (and conclusions)

With grounded semantics:




With preferred 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
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
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.
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.
A game tree
A
F
B
C
D
E
A game tree
A
F
B
C
D
E
P: A
A game tree
A
P: A
F
O: F
B
C
D
E
A game tree
A
P: A
F
O: F
B
P: E
C
D
E
A game tree
A
P: A
F
O: F
B
P: E
C
D
E
O: B
A game tree
A
P: A
F
O: B
O: F
B
P: E
C
D
E
P: C
A game tree
A
P: A
F
O: B
O: F
B
P: E
C
P: C
E
O: D
D
A game tree
A
P: A
F
O: B
O: F
B
P: E
C
P: C
E
O: D
D
P: E
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
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)
ASPIC system:
structure of arguments

An argument A is:

 if   K with



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) = 
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
P
Q1,R1,R2  K
Q1
Q1, Q2  P
Q2
R1
R1, R2  Q2
R2
Domain-specific vs. inference
general inference rules Flies



R1: Bird  Flies
R2: Penguin  Bird
Penguin  K
Bird
Penguin





R1: ,     
Strict rules: all deductively
valid inference rules
Bird  Flies  K
Bird
Penguin  Bird  K
Penguin  K
Penguin
Flies
Bird Flies
Penguin  Bird
ASPIC system:
attack and defeat


≥ is a preference ordering between arguments such
that if A is strict and B is defeasible then A > B
A rebuts B if




A undercuts B if



Conc(A) = ¬Conc(B’ ) for some B’  Sub(B); and
B’ applies a defeasible rule; and
not B’ > A
Naming convention
implicit
Conc(A) = ¬B’ for some B’  Sub(B); and
B’ applies a defeasible rule
A defeats B if A rebuts or undercuts B
P
Q1
Q2
Q2
R1
R2
V1
V2
S2
V3
T1
T2
Argument acceptability

Dung-style semantics and proof theory
directly apply!
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

1.
2.


closed under RS;
consistent if K is consistent
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)
Argument schemes:
general form
Premise 1,
…,
Premise n
Therefore (presumably), conclusion

But also critical questions

Negative answers are counterarguments
Expert testimony
(Walton 1996)
E is expert on D
E says that P
P is within D
Therefore (presumably), P is the case

Critical questions:



Is E biased?
Is P consistent with what other experts say?
Is P consistent with known evidence?
Witness testimony
Witness W says P
Therefore (presumably), P

Critical questions:



Is W sincere? (veracity)
Was P evidenced by W’s senses? (objectivity)
Did P occur? (observational sensitivity)
Perception
P is observed
Therefore (presumably), P

Critical questions:


Are the circumstances such that reliable
observation of P is impossible?
…
Memory
P is recalled
Therefore (presumably), P

Critical questions:


Was P originally based on beliefs of which
one is false?
…
‘Unpacking’ the witness
testimony scheme
Witness
testimony
Witness W says “I remember I saw P”
Therefore (presumably), W remembers he saw P
Therefore (presumably), W saw P
Witness
Therefore (presumably), P
testimony

Critical questions:



Is W sincere? (veracity)
Was P evidenced by W’s senses?
(objectivity)
Did P occur? (observational sensitivity)
‘Unpacking’ the witness
testimony scheme
Memory
Witness W says “I remember I saw P”
Therefore (presumably), W remembers he saw P
Therefore (presumably), W saw P
Therefore (presumably), P

Memory
Critical questions:



Is W sincere? (veracity)
Was P evidenced by W’s senses?
(objectivity)
Did P occur? (observational sensitivity)
‘Unpacking’ the witness
testimony scheme
Witness W says “I remember I saw P”
Therefore (presumably), W remembers he saw P
Perception
Therefore (presumably), W saw P
Therefore (presumably), P

Critical questions:


Perception

Is W sincere? (veracity)
Was P evidenced by W’s senses?
(objectivity)
Did P occur? (observational sensitivity)
Applying commonsense
generalisations
Consc of Guilt
P
If P then usually Q
Therefore (presumably), Q
Fleas
If Fleas then usually
Consc of Guilt
People who flea from a crime scene usually have consciousness 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
…
Arguments from consequences
Action A brings about G,
G is good (bad)
Therefore (presumably), A should (not) be done

Critical questions:



Does A also have bad (good) consequences?
Are there other ways to bring about G?
...
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
...
Part 2:
Dialogue
‘Argument’ is ambiguous

Inferential structure




Single agents
(Nonmonotonic) logic
Fixed information state
Form of dialogue



Multiple agents
Dialogue theory
Changing information state
Example
P: Tell me all you know about recent trading
in explosive materials (request)
P: why don’t you want to tell me?
P: why aren’t 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 won’t (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
don’t exchange the information with
other police officers (offer)
Example
P: Tell me all you know about recent trading
in explosive materials (request)
P: why don’t you want to tell me?
P: why aren’t 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 won’t (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
don’t exchange the information with
other police officers (offer)
Example
P: Tell me all you know about recent trading
in explosive materials (request)
P: why don’t you want to tell me?
P: why aren’t 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 won’t (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
don’t exchange the information with
other police officers (offer)
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
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
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 agent’s commitments)
Termination and outcome rules
Negotiation



Dialogue goal: making a deal
Participants’ goals: maximise individual
gain
Typical communication language:

Request p, Offer p, Accept p, Reject p, …
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
Standards for dialogue systems

Argument games: soundness and

Dialogue systems:
completeness wrt some logical
semantics

Effectiveness wrt dialogue goal


Efficiency, relevance, termination, ...
Fairness wrt participants’ goals

Can everything relevant be said?, ...
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?
...
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()
-
-
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
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
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
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: Concede Exception to R1
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
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
O: Concede Exception to R1
O: Retract
Not allowed to tell
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
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
claim
Not allowed to tell
claim
Not allowed to tell
why
claim
Not allowed to tell
why
since
Telling endangers
investigation
R1: What endangers an
investigation is not allowed
claim
Not allowed to tell
why
since
Telling endangers
investigation
concede
R1: What endangers an
investigation is not allowed
claim
why
Not allowed to tell
since
concede
Telling endangers
investigation
R1: What endangers an
investigation is not allowed
Exception to R1
R2: national
importance
 Not R1
since
National importance
claim
why
Not allowed to tell
since
concede
Telling endangers
investigation
R1: What endangers an
investigation is not allowed
Exception to R1
since
why
R2: national
importance
 Not R1
National importance
claim
why
Not allowed to tell
since
concede
Telling endangers
investigation
R1: What endangers an
investigation is not allowed
Exception to R1
since
why
R2: national
importance
 Not R1
National importance
since
Terrorist threat
Terrorist threat 
national importance
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
R2: national
importance
 Not R1
National importance
since
Terrorist threat
Terrorist threat 
national importance
claim
why
Not allowed to tell
retract
since
Telling endangers
investigation
concede
R1: What endangers an
investigation is not allowed
concede
Exception to R1
since
why
R2: national
importance
 Not R1
National importance
since
Terrorist threat
Terrorist threat 
national importance
Research issues

Investigation of protocol properties


Combinations of dialogue types




Mathematical proof or experimentation
Deliberation!
Multi-party dialogues
Dialogical agent behaviour (strategies)
...
Further information

http://people.cs.uu.nl/henry/siks/siks09.html