Abs12-argumentation Shish Mba Sams Ibm Varanasi

Introduction Argumentation Argumentation dialogue systems Summary

Introduction Argumentation Argumentation dialogue systems Summary

Where are we? Agent-Based Systems Semester 2, 2008-09

Last time . . .

Michael Rovatsos [email protected]

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Mechanism design & automated negotiation

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Protocols for reaching agreement

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Properties of such protocols

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Auction protocols and their properties

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Automated negotiation

Today . . . Lecture 4 – Deductive Reasoning Agents 22nd January 2009

Informatics UoE

Introduction Argumentation Argumentation dialogue systems Summary

Agent-Based Systems

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Introduction Argumentation Argumentation dialogue systems Summary

Logic-based argumentation

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Logic-based argumentation

1. Logical mode (deductive, proof-like, concerned with making correct inferences)

It is often not clear why agreement was reached Hard to explain to human user how they got best deal With a better understanding, the other might make more useful concessions

2. Emotional mode (appeals to feelings, attitudes, etc.) 3. Visceral mode (physical, social aspects)

Positions cannot be changed ◮

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Different modes of argument

Game-theoretic negotiation has its advantages But also some problems Positions cannot be justified ◮

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Game-theoretic negotiation – Limitations ◮

Argumentation in Multiagent Systems

4. Kisceral mode (appeals to the intuitive, mystical or religious)

Utilities don’t change as we negotiate We cannot model belief change with new information In case of irrational behaviour, no methods for recovery

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Different types are used in different situations (e.g. logical mode (hopefully) in courts of law)

Limitations give rise to argumentation-based negotiation (exchange of propositions to convince other of truth or falsity of certain facts) Informatics UoE

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Introduction Argumentation Argumentation dialogue systems Summary

Introduction Argumentation Argumentation dialogue systems Summary

Logic-based argumentation

Logic-based argumentation ◮

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Logic-based argumentation

“Purest”, most rational kind of argument: in classical logic, argument = sequence of inferences leading to a conclusion Write ∆ ⊢ ϕ to denote that sequence of inference steps from premises ∆ will allow us to establish proposition ϕ Example argument: ∆ ⊢ mortal (Socrates) where

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Database provides agreed common ground

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Agents make arguments of the form hSentence, Groundsi in support of Sentence

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Formal model: let ∆ a database, set of all arguments A(∆) contains pairs Arg = hϕ, Γi, Γ ⊆ ∆ are grounds/support for argument Γ ⊢ ϕ

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Idea: establish whether or not a set of arguments are in favour of some proposition Two important classes of arguments:

∆ = {human(Socrates), human(X ) ⇒ mortal(X )} ◮

Consider arguments of the form Database ⊢ hSentence, Groundsi where ◮ ◮ ◮

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Database is a possibly inconsistent set of logical formulae Sentence is a logical formula (the conclusion) Grounds is a set of logical formulae with Grounds ⊆ Database and Grounds ⊢ Sentence Informatics UoE

Introduction Argumentation Argumentation dialogue systems Summary

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Introduction Argumentation Argumentation dialogue systems Summary

Logic-based argumentation

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Logic-based argumentation

Logic-based argumentation

ϕ attacks ψ iff ϕ ≡ ¬ψ hϕ1 , Γ1 i rebuts hϕ2 , Γ2 i if ϕ1 attacks ϕ2 hϕ1 , Γ1 i undercuts hϕ2 , Γ2 i if ϕ1 attacks some ψ ∈ Γ2 hϕ1 , Γ1 i defeats hϕ2 , Γ2 i if it undercuts or rebuts it Example:

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Define argument Arg1 = hmortal(Heracles), {human(Heracles), human(X ) ⇒ mortal(X )}i

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Rebutting argument for Arg1 Arg2 = h¬mortal(Heracles), {father (Heracles, Zeus), father (X , Zeus) ⇒ divine(X ), divine(X ) ⇒ ¬mortal(X )}i

human(Hercules) father (Heracles, Zeus) father (Apollo, Zeus)

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father (X , Zeus) ⇒ divine(X ) ¬(father (X , Zeus) ⇒ divine(X ))

Agent-Based Systems

Arg2 undercut by Arg3 = h¬(father (X , Zeus) ⇒ divine(X )), {¬(father (X , Zeus) ⇒ divine(X ))}i

divine(X ) ⇒ ¬mortal(X )

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Non-trivial arguments: hϕ, Γi where Γ consistent Tautological arguments: hϕ, Γi where Γ = ∅

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Logic-based argumentation ◮

Logic-based argumentation

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Next, we define an ordering on “power” of arguments For example, if ∆ = {p ⇒ q, p}, hp ∨ ¬p, ∅i is intuitively stronger than hq, {p ⇒ q, p}i Informatics UoE

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Introduction Argumentation Argumentation dialogue systems Summary

Introduction Argumentation Argumentation dialogue systems Summary

Logic-based argumentation

Logic-based argumentation ◮

Logic-based argumentation

We can identify five classes of argument type in order of increasing acceptability

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A1: The class of all arguments that can be constructed from ∆

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A2: The class of all non-trivial arguments that can be constructed from ∆

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A3: The class of all arguments that can be constructed from ∆ with no rebutting arguments

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A4: The class of all arguments that can be constructed from ∆ with no undercutting arguments

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A5: The class of all tautological arguments that can be constructed from ∆ Informatics UoE

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hdivine(Heracles) ∨ ¬divine(Heracles), ∅i is in A5

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h¬mortal (apollo), {father (apollo, Zeus), father (X , Zeus) ⇒ divine(X ), divine(X ) ⇒ ¬mortal (X )}i is in A4 (if we assume that no undercutting arguments are allowed that can be attacked

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This model is widely used in argumentation-based systems

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Idea: convince the other agent to carry out some task for you by arguing for him actually intending to carry it out

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Abstract argumentation Implemented argumentation agents

Types of dialogue Typology due to Walton and Krabbe (1995):

Agent 0 attempts to convince 1 of some argument Agent 1 attempts to rebut or undercut it Agent 0 in turn attempts to defeat 1’s argument And so on . . .

Type Persuasion Negotiation Inquiry Deliberation Information seeking Eristics

Moves hPlayer , Arg i are steps in such a dialogue, Player ∈ {0, 1}, Arg ∈ A(∆) A sequence hm0 , . . . mk i is a dialogue history if ◮

In the above examples, Arg1 and Arg2 are mutually rebutting and thus in A2

Abstract argumentation Implemented argumentation agents

Now we turn to defining argumentation dialogues in which agents try to win an argument Call agents 0 and 1, assume following structure: ◮

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Argumentation dialogue systems ◮

Logic-based argumentation

Player2i = 0, Player2i +1 for all i ≥ 0 Argi +2 6= Argi , Argi +1 defeats Argi for all i ≥ 0

Initial situation conflict of opinion conflict of interest general ignorance need for action personal ignorance

Main goal resolve the issue make a deal growth of knowledge reach a decision spread knowledge

conflict/antagonism

reaching tion

accommoda-

Participants’ aim persuade other get best deal find a proof influence outcome gain or pass on knowledge strike other party

A dialogue ends if no further moves are possible, the winner is Playerk Informatics UoE

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Introduction Argumentation Argumentation dialogue systems Summary

Introduction Argumentation Argumentation dialogue systems Summary

Abstract argumentation Implemented argumentation agents

Abstract argumentation

Abstract argumentation

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There is a more abstract way of looking at argumentation

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Discard logical content of arguments and look just at relationships between them (Dung, 1995) An abstract argumentation system A = hX , →i is defined by

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Abstract argumentation Implemented argumentation agents

a set of arguments X (just a collection of objects), →⊆ X × X a binary attack relation on arguments

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Question: when is an argument “safe” (i.e. acceptable)?

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We discuss one way of modelling this

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x is attacked by a set of arguments Y ⊆ X if ∃y ∈ Y .y → x

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x is acceptable (“in”) wrt Y ⊆ X if every attacker of x (in X ) is also attacked by Y

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We write x → y as shorthand for (x, y ) ∈→ (“argument x attacks argument y ”)

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Y ⊆ X is conflict-free if no argument in Y attacks some other argument in Y

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We are not concerned with content of arguments or origin of “attack” relationship

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Y is admissible if it is conflict-free and each argument in Y is acceptable with respect to Y

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Introduction Argumentation Argumentation dialogue systems Summary

Introduction Argumentation Argumentation dialogue systems Summary

Abstract argumentation Implemented argumentation agents

Example ◮

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Abstract argumentation Implemented argumentation agents

Example

Abstract argumentation example c

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Argument h has no attackers

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Because of this, a is not acceptable

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For same reason p is out

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p only attacker of q, thus q is “in”

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As concerns i and j, at least one of them must be in

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Both attack n, so n has one undefeated attacker

i e n

“out”

“out”

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h

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“in”

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Introduction Argumentation Argumentation dialogue systems Summary

Introduction Argumentation Argumentation dialogue systems Summary

Abstract argumentation Implemented argumentation agents

Implemented argumentation agents ◮

Example: PERSUADER system for labour negotiation domain

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Agents: labour union, company, mediator

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Purpose: to reach agreement by exchanging proposals and counter-proposals

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Agents model each other’s beliefs

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Example argument: If the company is forced to grant higher wage increases, then it will decrease employment Argument types (in order of increasing “severity”)

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Implemented argumentation agents PERSUADER belief structure example (company perspective): profits(+)

production cost(−)

Agent-Based Systems

economic concessions (+)

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Logic-based negotiation: attacks, defeats

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Strengths of arguments

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Abstract argumentation systems

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(Implemented) argumentation dialogue systems

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Next time: Cooperative Distributed Problem Solving

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Agent-Based Systems

employment (−)

uneconomic concessions (+)

prices (−)

labour cost (−)

automation (+)

economic concessions (−)

subcontract (+)

wages(−)

fringes(−)

wages(+)

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Summary

Argumentation: a richer form of negotiation

materials cost(−)

employee satisfaction (+)

Introduction Argumentation Argumentation dialogue systems Summary

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sales(+) quality (+)

plant efficiency (+)

appeal to universal principle, appeal to a theme, appeal to authority, appeal to “status quo”, appeal to “minor standards”, appeal to “prevailing practice”, appeal to precedents as counter-examples, threaten Informatics UoE

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