Implementing Ranking-Based Semantics in ConArg
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The document discusses the implementation of ranking-based semantics in argumentation frameworks, detailing various types such as extension-based and labeling-based semantics. It includes analysis of power indexes like Shapley and Banzhaf indices, and their properties related to argument evaluations. The work is aimed at providing tools and understanding for analysis within argumentation theory.
Implementing Ranking-Based Semantics in ConArg
- 1. IMPLEMENTING RANKING-BASED SEMANTICS IN CONARG Stefano Bistarelli, Francesco Faloci, Francesco Santini and Carlo Taticchi
- 2. Implementing Ranking-Based Semantics in ConArg Carlo Taticchi — November 5, 2019 INDEX ▸ Argumentation Theory ▸ Argumentation Semantics ▸ Power Indexes ▸ Definitions ▸ PI-based semantics ▸ Description + Example ▸ Conclusion 2 ConArg
- 3. Implementing Ranking-Based Semantics in ConArg Carlo Taticchi — November 5, 2019 ABSTRACT ARGUMENTATION FRAMEWORKS1 3 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.
- 4. Implementing Ranking-Based Semantics in ConArg Carlo Taticchi — November 5, 2019 EXTENSION-BASED SEMANTICS 4 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}}
- 5. Implementing Ranking-Based Semantics in ConArg Carlo Taticchi — November 5, 2019 LABELLING-BASED SEMANTICS2 5 a b c d e 2Martin Caminada. On the Issue of Reinstatement in Argumentation. JELIA 2006: 111-123.
- 6. Implementing Ranking-Based Semantics in ConArg Carlo Taticchi — November 5, 2019 LABELLING-BASED SEMANTICS2 6 a b c d e 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.
- 7. Implementing Ranking-Based Semantics in ConArg Carlo Taticchi — November 5, 2019 7 a b c d e WHICH IS THE BEST? LABELLING-BASED SEMANTICS2
- 8. Implementing Ranking-Based Semantics in ConArg Carlo Taticchi — November 5, 2019 RANKING-BASED SEMANTICS3 ▸ Transforms an Argumentation Framework into a ranking ▸ Criteria: direct attacks, lengths of the incoming paths, rewards ▸ Good properties 8 3Leila Amgoud, Jonathan Ben-Naim. Ranking-Based Semantics for Argumentation Frameworks. SUM 2013: 134-147. ≻ a d ≻c ≻e ≻ b
- 9. Implementing Ranking-Based Semantics in ConArg Carlo Taticchi — November 5, 2019 ▸ Abstraction ▸ Independence ▸ Void Precedence ▸ Self-contradiction RANKING-BASED SEMANTICS - PROPERTIES4 ▸ Cardinality Precedence ▸ Quality Precedence ▸ Non-attacked Equivalence ▸ Totality 9 4Elise Bonzon, Jérôme Delobelle, Sébastien Konieczny, Nicolas Maudet. A Comparative Study of Ranking-Based Semantics for Abstract Argumentation. AAAI 2016: 914-920.
- 10. Implementing Ranking-Based Semantics in ConArg Carlo Taticchi — November 5, 2019 POWER INDEXES ▸ Shapley Value ▸ Banzhaf Index ▸ Deegan-Packel ▸ Johnstone 10
- 11. Implementing Ranking-Based Semantics in ConArg Carlo Taticchi — November 5, 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 11
- 12. Implementing Ranking-Based Semantics in ConArg Carlo Taticchi — November 5, 2019 vI σ,F(S) = { 1, if S ∈ in(Lσ) 0, if otherwise RANKING FUNCTIONS 12 a b c d e
- 13. Implementing Ranking-Based Semantics in ConArg Carlo Taticchi — November 5, 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 13 a b c d e
- 14. Implementing Ranking-Based Semantics in ConArg Carlo Taticchi — November 5, 2019 PI-BASED SEMANTICS 14 ∀a, b ∈ A, a ≻ b iff ∙ ϕa(vI σ,F) > ϕb(vI σ,F), or ∙ ϕa(vI σ,F) = ϕb(vI σ,F) and ϕa(vO σ,F) < ϕb(vO σ,F) ∀a, b ∈ A, a ≃ b iff ∙ ϕa(vI σ,F) = ϕb(vI σ,F) and ϕa(vO σ,F) = ϕb(vO σ,F)
- 15. Implementing Ranking-Based Semantics in ConArg Carlo Taticchi — November 5, 2019 EXAMPLE 15 a b c d e
- 16. Implementing Ranking-Based Semantics in ConArg Carlo Taticchi — November 5, 2019 16 PI-BASED SEMANTICS PROPERTIES a b c d e
- 19. Implementing Ranking-Based Semantics in ConArg Carlo Taticchi — November 5, 2019 CONARG WEB INTERFACE
- 20. Implementing Ranking-Based Semantics in ConArg Carlo Taticchi — November 5, 2019 CONCLUSION 20 ▸ Tool available at www.dmi.unipg.it/conarg ▸ Ranking-based semantics • Shapley Value • Banzhaf Index • Deegan-Packel • Johnstone
- 21. Implementing Ranking-Based Semantics in ConArg Carlo Taticchi — November 5, 2019 NEXT CONCLUSION 21 ▸ 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
- 22. IMPLEMENTING RANKING-BASED SEMANTICS IN CONARG Thanks for your attention!