Commonsense Reasoning and Argumentation 14/15 HC 14: Dialogue systems for argumentation (2) Henry Prakken 30 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) ActsAttacked bySurrendered by claim pwhy pconcede p why pArgue A (Conc(A) = p) retract p concede p retract p Argue AArgue B (defeats its target) Why p (p  Prem(A)) concede A concede 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)

 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 contractno 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

safe claim

safe claimwhy

safe airbag airbag  safe claimwhy since

safe airbag airbag  safe claimwhy since concede

safe airbag airbag  safe  safe newspaper newspaper   safe claimwhy since concede since

safe airbag airbag  safe  safe newspaper newspaper   safe claimwhy since concede since concede

safe airbag airbag  safe  safe newspaper newspaper   safe so what unreliable unreliable  so what claimwhy 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 claimwhy 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 retract claimwhy since concede since concede 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  q s   q r   s r, t   p Knowledge basesInference rules P1: q since p

Game for grounded semantics unsound in distributed settings Paul: p, r Olga: s, t Knowledge basesInference rules P1: q since p O1:  q since s p  q s   q r   s r,t   p

Game for grounded semantics unsound in distributed settings Paul: p, r Olga: s,t, r Knowledge basesInference rules P1: q since p O1:  q since s P2:  s since r p  q s   q r   s r,t   p

Game for grounded semantics unsound in distributed settings Paul: p, r Olga: s,t, r Knowledge basesInference rules P1: q since p O1:  q since s O2:  p since r,t P2:  s since r p  q s   q r   s r,t   p

Paul: p, r, p ∧ r  q, q  s Knowledge bases: Inference rules: R d = { ,      } R s = 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 ActsAttacked bySurrendered by claim pwhy pconcede p why pArgue A (Conc(A) = p) retract p concede p retract p Argue AArgue B (defeats its target) Why p (p  Prem(A)) concede A concede 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 contractno payment notary’s docsigned by us Not notary’s doc seal forged

Owe 500 contractno 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: p q Olga: p q   p Knowledge basesInference rules P1: claim 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: p q Olga: p q   p Knowledge basesInference 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: p q Olga: p q   p Knowledge basesInference 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: p q Olga: p q   p Knowledge basesInference 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: p q Olga: p q   p Knowledge basesInference 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?