argumentation henry prakken siks basic course learning and reasoning may 26 th, 2009
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Argumentation
Henry PrakkenSIKS Basic Course
Learning and ReasoningMay 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
Increased productivity is good
We should not lower taxes
Lower taxes increase inequality
Increased inequality is bad
Lower taxes do not increase productivity
USA lowered taxes but productivity decreased
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
Lower taxes do not increase productivity
Prof. P says that …
USA lowered taxes but productivity decreased
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
Lower taxes do not increase productivity
Prof. P says that …
Prof. P has political ambitions
People with political ambitions are not objective
Prof. P is not objective
USA lowered taxes but productivity decreased
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
Lower taxes do not increase productivity
Prof. P says that …
Prof. P has political ambitions
People with political ambitions are not objective
Prof. P is not objective
USA lowered taxes but productivity decreased
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
Lower taxes do not increase productivity
Prof. P says that …
Prof. P has political ambitions
People with political ambitions are not objective
Prof. P is not objective
Increased inequality is good
Increased inequality stimulates competition
Competition is good
USA lowered taxes but productivity decreased
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
Increased productivity is good
We should not lower taxes
Lower taxes increase inequality
Increased inequality is bad
Lower taxes do not increase productivity
Prof. P says that …
Prof. P has political ambitions
People with political ambitions are not objective
Prof. P is not objective
Increased inequality is good
Increased inequality stimulates competition
Competition is good
USA lowered taxes but productivity decreased
A B
C 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:
But not with:
A B C
A B
Two solutions
Change conditions so that always a unique status assignment results
Use multiple status assignments:
and
A B C
A BA B
A B 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 B
C D E
Is B, D or E defended by S1?Is B or E defended by S2?
A problem(?) with grounded semantics
We have: We want(?):
A B
C
D
A B
C
D
A problem(?) with grounded semantics
A B
C
D
A = Frederic Michaud is French since he has a French nameB = Frederic Michaud is Dutch since he is a marathon skaterC = 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
A problem(?) with grounded semantics
A B
C
D
A = Frederic Michaud is French since Alice says soB = Frederic Michaud is Dutch since Bob says soC = 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
E = Alice and Bob are unreliable since they contradict each other
Multiple labellings
A B
C
D
A B
C
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 = . 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
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.
A B
C D 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
Admissible?
A B
C D 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
Admissible?
A B
C D 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
Admissible?
A B
C D 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
Admissible?
A B
C D 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
Preferred?S is preferred if it is maximally admissible
A B
C D 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
Preferred?S is preferred if it is maximally admissible
A B
C D 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
Preferred?S is preferred if it is maximally admissible
A B
C D 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
Grounded?S is groundeded if it is the smallest set s.t. A S iff S defends A
A B
C D 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
Grounded?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: 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
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
B
C
D
E
F
A game tree
P: AA
B
C
D
E
F
A game tree
P: AA
B
C
D
E
F
O: F
A game tree
P: AA
B
C
D
E
F
O: F
P: E
A game tree
P: A
O: B
A
B
C
D
E
F
O: F
P: E
A game tree
P: A
O: B
P: C
A
B
C
D
E
F
O: F
P: E
A game tree
P: A
O: B
P: C
O: D
A
B
C
D
E
F
O: F
P: E
A game tree
P: A
O: B
P: C P: E
O: D
A
B
C
D
E
F
O: F
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
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
Q1 Q2
P
R1 R2
R1, R2 Q2
Q1, Q2 P
Q1,R1,R2 K
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
Flies
Bird
Penguin
Flies
Bird Bird Flies
Penguin 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 Conc(A) = ¬Conc(B’ ) for some B’ Sub(B); and B’ applies a defeasible rule; and not B’ > 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
Q1 Q2
P
R1 R2
Q2
V 1 V 2
V 3
S 2
T 1 T 2
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:
1. If B Sub(A) and A E then B E2. 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
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
But also critical questions Negative answers are counterarguments
Premise 1, … , Premise nTherefore (presumably), conclusion
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 DE says that PP is within D Therefore (presumably), P is the case
Witness testimony
Critical questions: Is W sincere? (veracity) Was P evidenced by W’s senses? (objectivity) Did P occur? (observational sensitivity)
Witness W says PTherefore (presumably), P
Perception
Critical questions: Are the circumstances such that reliable
observation of P is impossible? …
P is observedTherefore (presumably), P
Memory
Critical questions: Was P originally based on beliefs of
which one is false? …
P is recalledTherefore (presumably), P
‘Unpacking’ the witness testimony scheme
Critical questions: Is W sincere? (veracity) Was P evidenced by W’s senses?
(objectivity) Did P occur? (observational sensitivity)
Witness W says “I remember I saw P”Therefore (presumably), W remembers he saw PTherefore (presumably), W saw PTherefore (presumably), P
Witness testimony
Witness testimony
‘Unpacking’ the witness testimony scheme
Critical questions: Is W sincere? (veracity) Was P evidenced by W’s senses?
(objectivity) Did P occur? (observational sensitivity)
Witness W says “I remember I saw P”Therefore (presumably), W remembers he saw PTherefore (presumably), W saw PTherefore (presumably), P
Memory
Memory
‘Unpacking’ the witness testimony scheme
Critical questions: Is W sincere? (veracity) Was P evidenced by W’s senses?
(objectivity) Did P occur? (observational sensitivity)
Witness W says “I remember I saw P”Therefore (presumably), W remembers he saw PTherefore (presumably), W saw PTherefore (presumably), P
Perception
Perception
Applying commonsense generalisations
Critical questions: are there exceptions to the generalisation?
exceptional classes of people may have other reasons to flea Illegal immigrants Customers of prostitutes …
PIf P then usually QTherefore (presumably), Q
People who flea from a crime scene usually have consciousness of guilt
Consc of Guilt
Fleas If Fleas then usually Consc of Guilt
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
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 youO: 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 youO: 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 youO: 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
completeness wrt some logical semantics
Dialogue systems: 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 formalisedO: 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: Why National importance?
P: National importance since Terrorist threat &Terrorist threat National importance
P: Exception to R1 since National importance & National importance Exception to R1
Persuasion part formalisedO: 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: Why National importance?
P: National importance since Terrorist threat &Terrorist threat National importance
P: Exception to R1 since National importance & National importance Exception to R1
P: Concede Exception to R1
Persuasion part formalisedO: 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: Why National importance?
P: National importance since Terrorist threat &Terrorist threat National importance
P: Exception to R1 since National importance & National importance Exception to R1
O: Concede Exception to R1
O: Retract Not allowed to tell
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
Not allowed to tellclaim
Not allowed to tellclaim why
Not allowed to tell
Telling endangersinvestigation
R1: What endangers aninvestigation is not allowed
claim why
since
Not allowed to tell
Telling endangersinvestigation
R1: What endangers aninvestigation is not allowed
claim why
sinceconcede
Not allowed to tell
Telling endangersinvestigation
R1: What endangers aninvestigation is not allowed
Exception to R1
claim why
since
since
National importance R2: national importance
Not R1
concede
Not allowed to tell
Telling endangersinvestigation
R1: What endangers aninvestigation is not allowed
Exception to R1
claim why
since
since
National importance R2: national importance
Not R1
why
concede
Not allowed to tell
Telling endangersinvestigation
R1: What endangers aninvestigation is not allowed
Exception to R1
claim why
since
since
National importance R2: national importance
Not R1
Terrorist threat national importance
Terrorist threat
why
since
concede
Not allowed to tell
Telling endangersinvestigation
R1: What endangers aninvestigation is not allowed
Exception to R1
claim why
since
since
National importance R2: national importance
Not R1
Terrorist threat national importance
Terrorist threat
why
since
concede
concede
Not allowed to tell
Telling endangersinvestigation
R1: What endangers aninvestigation is not allowed
Exception to R1
claim why
since
since
National importance R2: national importance
Not R1
Terrorist threat national importance
Terrorist threat
why
since
concede
concederetract
Research issues Investigation of protocol properties
Mathematical proof or experimentation Combinations of dialogue types
Deliberation! Multi-party dialogues Dialogical agent behaviour (strategies) ...
Further information http://people.cs.uu.nl/henry/siks/
siks09.html