A TOOL FOR RANKING ARGUMENTS THROUGH VOTING-GAMES POWER INDEXES - - PowerPoint PPT Presentation

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A TOOL FOR RANKING ARGUMENTS THROUGH VOTING-GAMES POWER INDEXES - - PowerPoint PPT Presentation

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A TOOL FOR RANKING ARGUMENTS THROUGH VOTING-GAMES POWER INDEXES Stefano Bistarelli, Francesco Faloci, Francesco Santini and Carlo Taticchi INDEX Argumentation Theory Argumentation Semantics Power Indexes Definitions SV-based

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A TOOL FOR RANKING ARGUMENTS THROUGH VOTING-GAMES POWER INDEXES

Stefano Bistarelli, Francesco Faloci, Francesco Santini and Carlo Taticchi

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A Tool For Ranking Arguments Through Voting-Games Power Indexes Carlo Taticchi — June 20, 2019

INDEX

▸ Argumentation Theory

▸ Argumentation Semantics

▸ Power Indexes

▸ Definitions

▸ SV-based semantics

▸ Description + Example

▸ Conclusion

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ConArg

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A Tool For Ranking Arguments Through Voting-Games Power Indexes Carlo Taticchi — June 20, 2019

ABSTRACT ARGUMENTATION FRAMEWORKS1

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a b c d e

1Phan Minh Dung. On the acceptability of arguments and its fundamental role in nonmonotonic reasoning, logic programming and n-person
  • games. Artificial Intelligence, 77(2):321–357.
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A Tool For Ranking Arguments Through Voting-Games Power Indexes Carlo Taticchi — June 20, 2019

EXTENSION-BASED SEMANTICS

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a b c d e

ADM = {{}, {a}, {c}, {d}, {a, c}, {a, d}} CF = {{}, {a}, {b}, {c}, {d}, {a, c}, {a, d}, {b, d}} STA = {{a,d}} COM = {{a}, {a, c}, {a, d}}

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A Tool For Ranking Arguments Through Voting-Games Power Indexes Carlo Taticchi — June 20, 2019

LABELLING-BASED SEMANTICS2

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2Martin Caminada. On the Issue of Reinstatement in Argumentation. JELIA 2006: 111-123.
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A Tool For Ranking Arguments Through Voting-Games Power Indexes Carlo Taticchi — June 20, 2019

LABELLING-BASED SEMANTICS2

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IN if it is attacked only by OUT arguments OUT if it is attacked by at least an IN argument UNDEC otherwise

2Martin Caminada. On the Issue of Reinstatement in Argumentation. JELIA 2006: 111-123.
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A Tool For Ranking Arguments Through Voting-Games Power Indexes Carlo Taticchi — June 20, 2019

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WHICH IS THE BEST?

LABELLING-BASED SEMANTICS2

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A Tool For Ranking Arguments Through Voting-Games Power Indexes Carlo Taticchi — June 20, 2019

RANKING-BASED SEMANTICS3

▸ Transforms an Argumentation Framework into a ranking ▸ Criteria: direct attacks, lengths of the incoming paths, rewards ▸ Good properties

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3Leila Amgoud, Jonathan Ben-Naim. Ranking-Based Semantics for Argumentation Frameworks. SUM 2013: 134-147.

≻

a d ≻ c ≻e ≻ b

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A Tool For Ranking Arguments Through Voting-Games Power Indexes Carlo Taticchi — June 20, 2019

▸ Abstraction ▸ Independence ▸ Void Precedence ▸ Self-contradiction ▸ Cardinality Precedence

RANKING-BASED SEMANTICS - PROPERTIES4

▸ Quality Precedence ▸ Counter-Transitivity ▸ Strict Counter-Transitivity ▸ Defense Precedence ▸ Non-attacked Equivalence

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4Elise Bonzon, Jérôme Delobelle, Sébastien Konieczny, Nicolas Maudet. A Comparative Study of Ranking-Based Semantics for Abstract
  • Argumentation. AAAI 2016: 914-920.
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A Tool For Ranking Arguments Through Voting-Games Power Indexes Carlo Taticchi — June 20, 2019

POWER INDEXES

▸ Shapley Value ▸ Banzhaf Index ▸ Deegan-Packel ▸ Johnstone

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A Tool For Ranking Arguments Through Voting-Games Power Indexes Carlo Taticchi — June 20, 2019

▸ Banzhaf Index

ϕi(v) = ∑

S−i ⊆ G ∖ {i}

s!(n − 1 − s)! n! (v(S−i ∪ {i}) − v(S−i)) βi(v) = 1 2|N|−1 ∑

S ⊆ N ∖ {i}

(v(S ∪ {i}) − v(S))

▸ Shapley Value

POWER INDEXES

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A Tool For Ranking Arguments Through Voting-Games Power Indexes Carlo Taticchi — June 20, 2019

vI

σ,F(S) = {

1, if S ∈ in(Lσ) 0, if otherwise

RANKING FUNCTIONS

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A Tool For Ranking Arguments Through Voting-Games Power Indexes Carlo Taticchi — June 20, 2019

vI

σ,F(S) = {

1, if S ∈ in(Lσ) 0, if otherwise vO

σ,F(S) = {

1, if S ∈ out(Lσ) 0, if otherwise

RANKING FUNCTIONS

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In the event of a tie

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ConArg

www.dmi.unipg.it/conarg

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A Tool For Ranking Arguments Through Voting-Games Power Indexes Carlo Taticchi — June 20, 2019

SV-BASED SEMANTICS - PROPERTIES

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A Tool For Ranking Arguments Through Voting-Games Power Indexes Carlo Taticchi — June 20, 2019

SV-BASED SEMANTICS - PROPERTIES

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A Tool For Ranking Arguments Through Voting-Games Power Indexes Carlo Taticchi — June 20, 2019

SV-BASED SEMANTICS - PROPERTIES

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A Tool For Ranking Arguments Through Voting-Games Power Indexes Carlo Taticchi — June 20, 2019

SV-BASED SEMANTICS - PROPERTIES

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A Tool For Ranking Arguments Through Voting-Games Power Indexes Carlo Taticchi — June 20, 2019

SV-BASED SEMANTICS - PROPERTIES

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A Tool For Ranking Arguments Through Voting-Games Power Indexes Carlo Taticchi — June 20, 2019

CONCLUSION

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▸ Tool available at www.dmi.unipg.it/conarg ▸ Ranking-based semantics

  • Shapley Value
  • Banzhaf Index
  • Deegan-Packel
  • Johnstone
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A Tool For Ranking Arguments Through Voting-Games Power Indexes Carlo Taticchi — June 20, 2019

NEXT CONCLUSION

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▸ Understand the differences

between Power Indexes

▸ Capture global properties:

  • structure of the AF
  • full attacking paths

▸ Tool available at www.dmi.unipg.it/conarg ▸ Ranking-based semantics

  • Shapley Value
  • Banzhaf Index
  • Deegan-Packel
  • Johnstone
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A TOOL FOR RANKING ARGUMENTS THROUGH VOTING-GAMES POWER INDEXES Thanks for your attention!