argumentation henry prakken siks basic course learning and reasoning may 26 th, 2009

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 not lower taxes

Lower taxes increase inequality

Increased inequality is bad

Lower taxes do not increase productivity

USA lowered taxes but productivity decreased

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

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 …

Increased inequality is good

Increased inequality stimulates competition

Competition is good

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:

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:

Two solutions

Change conditions so that always a unique status assignment results

Use multiple status assignments:

A BA 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)

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 = 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 = 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 = Alice and Bob are unreliable since they contradict each other

Multiple labellings

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.

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

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.

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?

Preferred?S is preferred if it is maximally admissible

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

P: C 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

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

Penguin

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

V 1 V 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

Memory

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)

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

P: Concede 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

Not allowed to tell

claim why

sinceconcede

Not allowed to tell

Exception to R1

claim why

National importance R2: national importance

Not R1

concede

Not allowed to tell

Exception to R1

claim why

Not R1

concede

Not allowed to tell

Exception to R1

claim why

Not R1

Terrorist threat national importance

Terrorist threat

concede

Not allowed to tell

Exception to R1

claim why

Not R1

Terrorist threat

concede

Not allowed to tell

Exception to R1

claim why

Not R1

Terrorist threat

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

argumentation henry prakken siks basic course learning and reasoning may 26 th, 2009

lower taxes lower taxes

bad lower taxes

productivity usa

good increased inequality

objective increased

good slide

bad slide

inference slide

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