Commonsense Reasoning and Argumentation 14/15

HC 14:Dialogue systems for argumentation (2)

Henry Prakken30 March 2015

Contents Dialogue systems for

argumentation (2) Prakken’s dialogue system framework

Two systems for persuasion dialogue

Parsons, Wooldridge & Amgoud Journal of Logic and Computation

13(2003) Prakken

Journal of Logic and Computation 15(2005)

Prakken: languages, logic, agents

Lc: Any, provided it has a reply structure (attacks + surrenders)

Lt: any Logic: argumentation logic

ASPIC with grounded semantics Assumptions on agents: none.

Prakken: example Lc (with reply structure)

Acts Attacked by

Surrendered by

claim p why p concede p

why p Argue A(Conc(A) = p)

retract p

concede p

   

retract p    

Argue A Argue B(defeats its target)

Why p (p Prem(A))

concede Aconcede p (p Prem(A) or p = Conc(A))

Prakken: protocols (basic rules)

Each noninitial move replies to some previous move of hearer

Replying moves must be defined in Lc as a reply to their target

Termination: if player to move has no legal moves

… Outcome: what is dialogical status of

initial move at termination?

Dialogical status of moves

Each move in a dialogue is in or out: A surrender is out, An attacker is:

in if surrendered, else: in iff all its attackers are out out iff it has an attacker that is in

(An Argue A move is surrendered iff A’s conclusion is conceded)

Functions of dialogical status

Can determine winning Proponent wins iff at termination the initial claim is

in; opponent wins otherwise Can determine turntaking

Turn shifts if dialogical status of initial move has changed

Immediate response protocols Can be used in defining relevance

1: claim (owe $500)

1: claim (owe $500)

2: why (owe $500)

1: claim (owe $500)

2: why (owe $500)

4: argue (owe $500 since contract & no payment)

1: claim (owe $500)

2: why (owe $500)

4: argue (owe $500 since contract & no payment)

5: concede (no payment)

1: claim (owe $500)

2: why (owe $500)

4: argue (owe $500 since contract & no payment)

5: concede (no payment) 6: why (contract)

1: claim (owe $500)

2: why (owe $500)

4: argue (owe $500 since contract & no payment)

5: concede (no payment) 6: why (contract)

8: argue (contract since notary’s document & signed by us)

1: claim (owe $500)

2: why (owe $500)

4: argue (owe $500 since contract & no payment)

5: concede (no payment) 6: why (contract)

8: argue (contract since notary’s document & signed by us)

11: argue (notary’s document since notary’s seal is forged)

1: claim (owe $500)

2: why (owe $500)

4: argue (owe $500 since contract & no payment)

5: concede (no payment) 6: why (contract)

8: argue (contract since notary’s document & signed by us)

11: argue (notary’s document since notary’s seal is forged)

12: why (notary’s seal is forged)

1: claim (owe $500)

2: why (owe $500)

4: argue (owe $500 since contract & no payment)

5: concede (no payment) 6: why (contract)

8: argue (contract since notary’s document & signed by us)

11: argue (notary’s document since notary’s seal is forged)

12: why (notary’s seal is forged)

13: concede (owe $500))

Owe 500

contract no payment

notary’s docsigned by us Not notary’s doc

seal forged

Prakken: example dialogue

P1: claim safe

Prakken: example dialogue

P1: claim safe

O1: why safe

Prakken: example dialogue

P1: claim safe

O1: why safe

P2: safe since airbag,airbag safe

Prakken: example dialogue

P1: claim safe

O1: why safe

P2: safe since airbag,airbag safe

O2a: concede airbag

Prakken: example dialogue

P1: claim safe

O1: why safe

P2: safe since airbag,airbag safe

O2a: concede airbag O2b: safe since newspaper, newspaper safe

Prakken: example dialogue

P1: claim safe

O1: why safe

P2: safe since airbag,airbag safe

O2a: concede airbag O2b: safe since newspaper, newspaper safe

P3a: concede newspaper

Prakken: example dialogue

P1: claim safe

O1: why safe

P2: safe since airbag,airbag safe

O2a: concede airbag O2b: safe since newspaper, newspaper safe

P3a: concede newspaper P3b: so what since unreliable, unreliable so what

Prakken: example dialogue

P1: claim safe

O1: why safe

P2: safe since airbag,airbag safe

O2a: concede airbag O2b: safe since newspaper, newspaper safe

O3: safe since high speed, high speed safe

P3a: concede newspaper P3b: so what since unreliable, unreliable so what

Prakken: example dialogue

P1: claim safe

O1: why safe

P2: safe since airbag,airbag safe

O2a: concede airbag O2b: safe since newspaper, newspaper safe

O3: safe since high speed, high speed safe

P3a: concede newspaper P3b: so what since unreliable, unreliable so what

P4: retract safe

safeclaim

safeclaim why

safe

airbag airbag safe

claim why

since

safe

airbag airbag safe

claim why

since

concede

safe

airbag airbag safe

safe

newspaper newspaper safe

claim why

since

concede

since

safe

airbag airbag safe

safe

newspaper newspaper safe

claim why

since

concede

since

concede

safe

airbag airbag safe

safe

newspaper newspaper safe

so what

unreliable unreliable so what

claim why

since

concede

since

concede

since

safe

airbag airbag safe

safe

newspaper newspaper safe

safe

high speed high speed safe

so what

unreliable unreliable so what

claim why

since

concede

since

concede

since

since

safe

airbag airbag safe

safe

newspaper newspaper safe

safe

high speed high speed safe

so what

unreliable unreliable so what

retract

claim why

since

concede

since

concede

since

since

Relevant protocols

A reply must be relevant An attacking move is relevant if it changes the status

of the initial move A surrendering move is relevant if an attacking

counterpart is relevant (an attacking counterpart replies to the same (part

of) move) The turn shifts if dialogical status of initial

move has changed Immediate response protocols

P1+

O1-

P2- P4+

O2- O3+

P3+ Relevant target?

P1+

O1-

P2- P4+

O2+ O3+

P3-

O4+

P1+

O1-

P2- P4+

O2- O3+

P3+

Relevant target?

P1-

O1+

P2- P4-

O2- O3+

P3+

O4+

1: claim (owe $500)

2: why (owe $500)

4: argue (owe $500 since contract & no payment)

5: concede (no payment) 6: why (contract)

8: argue (contract since notary’s document & signed by us)

11: argue (notary’s document since notary’s seal is forged)

12: why (notary’s seal is forged)

What are the relevant targets for ?

1: claim (owe $500)

2: why (owe $500)

4: argue (owe $500 since contract & no payment)

5: concede (no payment) 6: why (contract)

8: argue (contract since notary’s document & signed by us)

11: argue (notary’s document since notary’s seal is forged)

12: why (notary’s seal is forged)

13: concede (owe $500))

What are the relevant targets for ?

Game for grounded semantics unsound in distributed settings

Paul: p, r

Olga: s, t

p qs qr sr, t p

Knowledge bases Inference rules

P1: q since p

Game for grounded semantics unsound in distributed settings

Paul: p, r

Olga: s, t

Knowledge bases Inference rules

P1: q since p

O1: q since s

p qs qr sr,t p

Game for grounded semantics unsound in distributed settings

Paul: p, r

Olga: s,t, r

Knowledge bases Inference rules

P1: q since p

O1: q since s

P2: s since r

p qs qr sr,t p

Game for grounded semantics unsound in distributed settings

Paul: p, r

Olga: s,t, r

Knowledge bases Inference rules

P1: q since p

O1: q since s

O2: p since r,t

P2: s since r

p qs qr sr,t p

Paul: p, r, p ∧r q,q s

Knowledge bases:

Inference rules:

Rd = {, }Rs = all valid inference rules of prop. l.

Olga: t, t p,p q

No preferences

Find a terminated legal dialogue of five moves with a relevant protocol won by Olga, assuming both are honest

Acts Attacked by

Surrendered by

claim p why p concede p

why p Argue A(Conc(A) = p)

retract p

concede p

   

retract p    

Argue A Argue B(defeats its target)

Why p (p Prem(A))

concede Aconcede p (p Prem(A) or p = Conc(A))

Winning and logic A protocol should respect the underlying logic We want: main claim is in iff it is implied by the

current ‘theory’ of the dialogue (all non-challenged and non-retracted ‘current’ premises)

Ensured in relevant protocols if No surrenders are moved; and Arguments cannot be weakened by ‘backwards

extending’ Each argument implied by the current theory has been

moved Current theory = all non-challenged and non-retractred

current premises

1: claim (owe $500)

2: why (owe $500)

4: argue (owe $500 since contract & no payment)

5: concede (no payment) 6: why (contract)

8: argue (contract since notary’s document & signed by us)

11: argue (notary’s document since notary’s seal is forged)

12: why (notary’s seal is forged)

13: concede (owe $500))

Owe 500

contract no payment

notary’s docsigned by us Not notary’s doc

seal forged

Owe 500

contract no payment

notary’s docsigned by us Not notary’s doc

seal forged

Prakken’s relevant protocols: characteristics

Protocol Multiple-move Multiple-reply Not deterministic in Lc Immediate-response

Dialogues Can be long (stepwise construction of arguments, alternative

replies) Both sides can develop arguments

Logic Used for single agent: construct/attack arguments Used in protocol

Commitments Not used (could be used in protocol)

Filibustering Many two-party protocols allow obstructive

behaviour: P: claim p O: why p? P: p since q O: why q? P: q since r O: why r? ...

Possible sanctions Social sanctions:

I don’t talk to you any more Shift of burden of proof by third

party ... P: q since r O: why r? referee: O, you must defend not-r!

Example 2

Paul: pq

Olga: pq p

Knowledge bases Inference rules

P1: claim pModus ponens

…

Paul Olga does not justify p but they will agree on p if players are

conservative, that is, if they stick to their beliefs if possible

Example 2

Paul: pq

Olga: pq p

Knowledge bases Inference rules

P1: claim p

O1: concede p

Modus ponens

…

Paul Olga does not justify p but they will agree on p if players are

conservative, that is, if they stick to their beliefs if possible

Example 2

Paul: pq

Olga: pq p

Knowledge bases Inference rules

P1: claim p

O1: what about q?

Modus ponens

…

Possible solution (for open-minded agents, who are

prepared to critically test their beliefs):

Example 2

Paul: pq

Olga: pq p

Knowledge bases Inference rules

P1: claim p

O1: what about q?

Modus ponens

…

P2: claim q

Possible solution (for open-minded agents, who are

prepared to critically test their beliefs):

Example 2

Paul: pq

Olga: pq p

Knowledge bases Inference rules

P1: claim p

O1: what about q?

Modus ponens

…

P2: claim q

O2: p since q, q p Possible solution (for open-minded agents, who are

prepared to critically test their beliefs):

Problem: how to ensure relevance?