Playing with Argumentation Nicolas Maudet nicolas.maudet@lip6.fr Universit´ e Pierre et Marie Curie EPCL-BTC: 19th of Novembre 2013
Outline of the talk MutliArg Nicolas Maudet UPMC Motivation 1 EPCL-BTC: 19th of Novembre 2013 Motivation Argumentation basics Argumentation 2 basics A multiparty protocol A multiparty protocol Properties 3 Challenges Properties 4 Challenges 5 2 / 38
Motivation: Online Debate Platforms MutliArg Nicolas Maudet UPMC EPCL-BTC: 19th of Novembre 2013 Motivation Argumentation basics A multiparty protocol Properties Challenges Figure: debategraph.org 3 / 38
Motivation: Online Debate Platforms MutliArg Nicolas Maudet UPMC EPCL-BTC: 19th of Some practical problems with these systems: Novembre 2013 Motivation ◮ the number of agents and arguments put forward give rise to Argumentation unfocused debates, difficult to follow and interpret basics A multiparty ◮ agents may have unequal access to the debate platform protocol Properties ◮ agents cannot be assumed to fully cooperative Challenges One approach is to rely on crowdsourcing. Here we take a more normative view and regulate the debate by means of a protocol. The resulting setting may be approached with game theoretical tools. 4 / 38
Argumentation and Game-Theory MutliArg Nicolas Maudet There are existing works relating argumentations and games, in UPMC particular: EPCL-BTC: 19th of Novembre 2013 ◮ proof-theoretical procedures involving an agent trying to defend an Motivation argument (PRO) and an agent trying to destroy this argument Argumentation basics (CON). A multiparty winning strategy = provability = x belongs to some/all extensions protocol Properties There also are existing works relating argumentation and non Challenges cooperative game-theoretical notions. But here we need to define the components of a game ◮ what are the goals of agents? ◮ what are the permitted moves? ◮ what is the winning criterion? 5 / 38
A two-agent example MutliArg Example: the argumentative battle of the sexes Nicolas Maudet Suppose the arguments of a a given argumentation system are UPMC EPCL-BTC: 19th of partitioned among two agents (blue and red): Novembre 2013 Motivation ◮ x 1 : we should go to a football match Argumentation basics ◮ x 2 : we should go to a ballet A multiparty ◮ x 3 : I can’t stay outside for a long time protocol Properties ◮ x 4 : my worst enemy goes to the ballet as well... Challenges What are the goals of agents? Assume agents have preferences on the possible extensions, possibly based on some goals they have. Take : ◮ blue : football ≻ ballet ≻ ∅ (say, 2,1,0 as utility) ◮ red : ballet ≻ football ≻ ∅ (say, 2,1,0 as utility) Rahwan and Larson. Argumentation and Game-Theory . Argumentation in AI. 6 / 38
A two-agent example MutliArg ◮ strategies: subsets of (his own) arguments to put forward Nicolas Maudet UPMC x 1 x 2 EPCL-BTC: 19th of Novembre 2013 Motivation Argumentation basics A multiparty protocol { x 1 } { x 4 } { x 1 , x 4 } {} Properties { x 2 } 0,0 0,0 1,2 2,1 x 3 x 4 Challenges { x 3 } 0,0 0,0 0,0 0,0 { x 2 , x 3 } 2,1 0,0 0,0 2,1 {} 1,2 0,0 1,2 0,0 ◮ { x 3 } and { x 4 } are weakly dominated. ◮ Nash equilibrium = no agent has an incentive to unilaterally deviate. Can you spot NE? 7 / 38
A two-agent example MutliArg ◮ strategies: subsets of (his own) arguments to put forward Nicolas Maudet UPMC x 1 x 2 EPCL-BTC: 19th of Novembre 2013 Motivation Argumentation basics A multiparty protocol { x 1 } { x 4 } { x 1 , x 4 } {} Properties { x 2 } 0,0 0,0 1,2 2,1 x 3 x 4 Challenges { x 3 } 0,0 0,0 0,0 0,0 { x 2 , x 3 } 2,1 0,0 0,0 2,1 {} 1,2 0,0 1,2 0,0 ◮ { x 3 } and { x 4 } are weakly dominated. ◮ Nash equilibrium = no agent has an incentive to unilaterally deviate. Can you spot NE? 7 / 38 �{ x 2 } , { x 1 , x 4 }� , �{ x 2 , x 3 } , { x 1 }� , �{} , { x 1 , x 4 }� , �{ x 2 , x 3 } , {}� , �{} , {}�
A two-agent setting MutliArg Nicolas Maudet However, this type of analysis is not highly relevant for the types of UPMC debates that we envision: EPCL-BTC: 19th of Novembre 2013 ◮ moves are not played simultaneously Motivation Argumentation ◮ and even a sequential analysis would be poorly relevant: basics • it is difficult to assume a predefined sequence of turns (round-robin A multiparty protocol protocol) when there are many agents Properties • it is difficult to assume full knowledge of the utility functions of the Challenges other agents An analysis in terms of dynamics of better/best responses is more appropriate. Bonzon and Maudet. On the outcomes of multiparty argumentation . AAMAS-11. 8 / 38
Outline of the talk MutliArg Nicolas Maudet UPMC Motivation 1 EPCL-BTC: 19th of Novembre 2013 Motivation Argumentation basics Argumentation 2 basics A multiparty protocol A multiparty protocol Properties 3 Challenges Properties 4 Challenges 5 9 / 38
Argumentation systems MutliArg Nicolas Maudet UPMC Abstract view of argumentation (no specification of the actual content EPCL-BTC: 19th of of arguments), due to [Dung, 95] Novembre 2013 Motivation ◮ Argumentation system AS defined as a pair Argumentation • A : set of arguments basics • R : attack relation ( ⊆ A × A ) A multiparty protocol The meaning of the attack relation is that an argument“defeats” Properties another argument. Challenges ◮ Argumentation graph AS = { a , b , c } , { ( b , c ) , ( a , b ) , ( a , c ) } P. M. Dung. On the Acceptability of Arguments and its Fundamental Role in Nonmonotonic Reasoning, Logic Programming and n -Person Games . AIJ, 1995. 10 / 38
Argumentation systems + Preferences 1. Label each argument according to the value it puts forward, or the MutliArg source it comes from, etc. Nicolas Maudet UPMC EPCL-BTC: 19th of a b c Novembre 2013 Motivation WKL NYT CHK Argumentation basics A multiparty protocol Properties Challenges 11 / 38
Argumentation systems + Preferences 1. Label each argument according to the value it puts forward, or the MutliArg source it comes from, etc. Nicolas Maudet UPMC EPCL-BTC: 19th of a b c Novembre 2013 Motivation WKL NYT CHK Argumentation basics A multiparty protocol 2. Discard attacks coming from less preferred values/sources ( “the Properties attack is not strong enough to defeat the argument” ) Challenges a b c WKL NYT CHK WKL ≻ CHK ≻ NYT 11 / 38 T. M. Bench-Capon. Value-based argumentation frameworks . NMR, 2002.
A Simple Example MutliArg Nicolas Maudet UPMC EPCL-BTC: 19th of Novembre 2013 Consider the following arguments: Motivation Argumentation (c) The US army is preparing a secret plan to retreat from basics Afghanistan (source: Wikileaks) A multiparty protocol (b) Our (informed) sources say the documents are fake. Properties (source: NYT) Challenges (a) The media cannot be trusted on military issues (source: N. Chomsky) 12 / 38
Why systems may differ MutliArg Nicolas Maudet UPMC EPCL-BTC: 19th of a b c a b c a b c Novembre 2013 Motivation Argumentation basics A multiparty ◮ a 1 thinks CHK is the more credible source, and sees WKL as a protocol Properties media (more credible than the NYT). Challenges ◮ a 2 thinks NYT is more credible than WKL, but that CHK is more credible than NYT. But he believes WKL cannot be seen as a media. ◮ a 3 thinks the NYT is the more credible source, and that CHK always says stupid things. 13 / 38
Acceptability MutliArg Nicolas Maudet UPMC Now we need to define what (sets of) arguments should be considered EPCL-BTC: 19th of as“justified”point of view. Novembre 2013 Many different ways to define this! ( ⇒ argumentation semantics) Motivation Argumentation ◮ S collectively defends a ∈ A iff ∀ b ∈ A such that bRa , ∃ c ∈ S basics A multiparty such that cRb protocol ◮ S is a grounded extension iff S is the least fixed point of the Properties Challenges characteristic function F of AS F ( S ) = { a such that S collectively defends a } ◮ always exists a unique grounded extension, denoted by E ( AS ) ◮ can be computed in polynomial time 14 / 38
Acceptablity: example MutliArg a b c a b c a b c Nicolas Maudet UPMC EPCL-BTC: 19th of Novembre 2013 ◮ a 1 thinks CHK is the more credible source, and sees WKL as a Motivation media (more credible than the NYT). Argumentation basics a 1 : E ( AS 1 ) = { a } A multiparty protocol Properties ◮ a 2 thinks NYT is more credible than WKL, but that CHK is more Challenges credible than NYT. But he believes WKL cannot be seen as a media. a 2 : E ( AS 2 ) = { a , c } ◮ a 3 thinks the NYT is the more credible source, and that CHK always say rubbish. 15 / 38 a 3 : E ( AS 3 ) = { a , b }
Assumptions MutliArg Nicolas Maudet Now suppose that these agents want to exchange their different points UPMC of view. How shall they proceed? EPCL-BTC: 19th of Novembre 2013 The following is taken for granted: Motivation Argumentation ◮ many agents debating basics ◮ a single issue is under discussion (focused agents) A multiparty protocol ◮ no coordination takes place among agents Properties Challenges ◮ agents agree on the set of (potential) arguments ◮ agents may disagree on the attack relations among these arguments And we stick to the Dung’s semantics (other approaches are possible). Martins and Leite. Social abstract argumentation . IJCAI-13. 16 / 38
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