Extending Labelling Semantics to Weighted Argumentation Frameworks
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This document summarizes a presentation on extending labelling semantics to weighted argumentation frameworks. It introduces: - Background on extension- and labelling-based semantics and weighted argumentation frameworks (WAFs). - A weighted labelling approach that accounts for weights using different notions of weighted defence. This includes weighted versions of conflict-free, admissible, preferred, complete, stable, and grounded labelling semantics. - An implementation of these weighted labelling semantics in a tool called ConArg. - Areas of future work, such as differentiating types of undecided labels and allowing empty labels.
Extending Labelling Semantics to Weighted Argumentation Frameworks
- 1. FLAIRS 2021 Extending Labelling Semantics to Weighted Argumentation Frameworks Stefano Bistarelli, Carlo Taticchi
- 2. FLAIRS 2021 - Extending Labelling Semantics to Weighted Argumentation Frameworks • Background: ‣ Extension- and Labelling-Based Semantics ‣ Weighted AFs • Weighted Labelling ‣ Di ff erent defences ‣ Semantics • Conclusion Overview 2
- 3. FLAIRS 2021 - Extending Labelling Semantics to Weighted Argumentation Frameworks Extension-based Semantics for AFs 3 Applications for Decision Making / Explainable ML
- 4. FLAIRS 2021 - Extending Labelling Semantics to Weighted Argumentation Frameworks Extension-based Semantics for AFs 3 Con fl ict-Free {a}, {c}, {a,d}, … Applications for Decision Making / Explainable ML
- 5. FLAIRS 2021 - Extending Labelling Semantics to Weighted Argumentation Frameworks Extension-based Semantics for AFs 3 Con fl ict-Free {a}, {c}, {a,d}, … Admissible {a, d}, {a, d, e}, … Applications for Decision Making / Explainable ML
- 6. FLAIRS 2021 - Extending Labelling Semantics to Weighted Argumentation Frameworks Extension-based Semantics for AFs 3 Con fl ict-Free {a}, {c}, {a,d}, … Admissible {a, d}, {a, d, e}, … Complete {a, b, d, e} Applications for Decision Making / Explainable ML
- 7. FLAIRS 2021 - Extending Labelling Semantics to Weighted Argumentation Frameworks IN if it is attacked only by OUT arguments OUT if it is attacked by at least an IN argument UNDEC otherwise Reinstatement Labelling 4
- 8. FLAIRS 2021 - Extending Labelling Semantics to Weighted Argumentation Frameworks Labelling-Based Semantics 5 a is IN a is not attacked by any IN a is OUT a is attacked by some IN CF
- 9. FLAIRS 2021 - Extending Labelling Semantics to Weighted Argumentation Frameworks Labelling-Based Semantics 6 a is IN a is only attacked by OUT a is OUT a is attacked by some IN ADM
- 10. FLAIRS 2021 - Extending Labelling Semantics to Weighted Argumentation Frameworks Labelling-Based Semantics 7 a is IN a is only attacked by OUT a is OUT a is attacked by some IN ⟺ ⟺ COM
- 11. FLAIRS 2021 - Extending Labelling Semantics to Weighted Argumentation Frameworks • The acceptability of the arguments also depends on the weights • Di ff erent notion of defence Weighted Argumentation Frameworks 8
- 12. FLAIRS 2021 - Extending Labelling Semantics to Weighted Argumentation Frameworks • The acceptability of the arguments also depends on the weights • Di ff erent notion of defence Weighted Argumentation Frameworks 8
- 13. FLAIRS 2021 - Extending Labelling Semantics to Weighted Argumentation Frameworks • The acceptability of the arguments also depends on the weights • Di ff erent notion of defence Weighted Argumentation Frameworks 8
- 14. FLAIRS 2021 - Extending Labelling Semantics to Weighted Argumentation Frameworks • The acceptability of the arguments also depends on the weights • Di ff erent notion of defence Weighted Argumentation Frameworks 8
- 15. FLAIRS 2021 - Extending Labelling Semantics to Weighted Argumentation Frameworks Weighted Defence (3) 9 w-defends : Def ⊆ Args d ∈ Args ⟺ ∀c ∈ Arg ∣ c → d Def = {a, b, d, e}
- 16. FLAIRS 2021 - Extending Labelling Semantics to Weighted Argumentation Frameworks Weighted Defence (3) 9 w-defends : Def ⊆ Args d ∈ Args ⟺ ∀c ∈ Arg ∣ c → d • D1 (📖 Martínez&al2008): ∃a ∈ Def |W(c, d) ≥S W(a, c) Def = {a, b, d, e}
- 17. FLAIRS 2021 - Extending Labelling Semantics to Weighted Argumentation Frameworks Weighted Defence (3) 9 w-defends : Def ⊆ Args d ∈ Args ⟺ ∀c ∈ Arg ∣ c → d • D1 (📖 Martínez&al2008): ∃a ∈ Def |W(c, d) ≥S W(a, c) Def = {a, b, d, e}
- 18. FLAIRS 2021 - Extending Labelling Semantics to Weighted Argumentation Frameworks Weighted Defence (3) 9 w-defends : Def ⊆ Args d ∈ Args ⟺ ∀c ∈ Arg ∣ c → d • D1 (📖 Martínez&al2008): ∃a ∈ Def |W(c, d) ≥S W(a, c) • D2 (📖 Coste-Marquis&al2012): W(c, d) ≥S W(Def, c) Def = {a, b, d, e}
- 19. FLAIRS 2021 - Extending Labelling Semantics to Weighted Argumentation Frameworks Weighted Defence (3) 9 w-defends : Def ⊆ Args d ∈ Args ⟺ ∀c ∈ Arg ∣ c → d • D1 (📖 Martínez&al2008): ∃a ∈ Def |W(c, d) ≥S W(a, c) • D2 (📖 Coste-Marquis&al2012): W(c, d) ≥S W(Def, c) Def = {a, b, d, e}
- 20. FLAIRS 2021 - Extending Labelling Semantics to Weighted Argumentation Frameworks Weighted Defence (3) 9 w-defends : Def ⊆ Args d ∈ Args ⟺ ∀c ∈ Arg ∣ c → d • D1 (📖 Martínez&al2008): ∃a ∈ Def |W(c, d) ≥S W(a, c) • D2 (📖 Coste-Marquis&al2012): W(c, d) ≥S W(Def, c) • D3 (📖 Bistarelli&al2016): W(c, Def ∪ {d}) ≥S W(Def, c) Def = {a, b, d, e}
- 21. FLAIRS 2021 - Extending Labelling Semantics to Weighted Argumentation Frameworks Weighted Defence (3) 9 w-defends : Def ⊆ Args d ∈ Args ⟺ ∀c ∈ Arg ∣ c → d • D1 (📖 Martínez&al2008): ∃a ∈ Def |W(c, d) ≥S W(a, c) • D2 (📖 Coste-Marquis&al2012): W(c, d) ≥S W(Def, c) • D3 (📖 Bistarelli&al2016): W(c, Def ∪ {d}) ≥S W(Def, c) Def = {a, b, d, e}
- 22. FLAIRS 2021 - Extending Labelling Semantics to Weighted Argumentation Frameworks • The w-con fl ict-free and the con fl ict-free labelling coincides Labelling-Based Semantics for WAFs 10 a is IN a is not attacked by any IN a is OUT a is attacked by some IN CF W-CF
- 23. FLAIRS 2021 - Extending Labelling Semantics to Weighted Argumentation Frameworks Labelling-Based Semantics for WAFs 11 is IN IN w-defends is OUT IN a ⟹ a− = a− |OUT ∧ Arg ↓ a a ⟹ W(a− ↓ , a) < 𝕊 ⊤ W-ADM D1 D2 D3
- 24. FLAIRS 2021 - Extending Labelling Semantics to Weighted Argumentation Frameworks Labelling-Based Semantics for WAFs 12 is IN IN w-defends is OUT IN a ⟹ a− = a− |OUT ∧ Arg ↓ a a ⟹ W(a− ↓ , a) < 𝕊 ⊤ W-ADM D1 D2 D3
- 25. FLAIRS 2021 - Extending Labelling Semantics to Weighted Argumentation Frameworks Labelling-Based Semantics for WAFs 13 is IN IN w-defends is OUT IN IN is maximal a ⟹ a− = a− |OUT ∧ Arg ↓ a a ⟹ W(a− ↓ , a) < 𝕊 ⊤ Arg ↓ W-PRF D1 D2 D3
- 26. FLAIRS 2021 - Extending Labelling Semantics to Weighted Argumentation Frameworks Labelling-Based Semantics for WAFs 14 D1 D2 D3 W-COM is IN IN w-defends is OUT IN a ⟺ a− = a− |OUT ∧ Arg ↓ a a ⟹ W(a− ↓ , a) < 𝕊 ⊤
- 27. FLAIRS 2021 - Extending Labelling Semantics to Weighted Argumentation Frameworks Labelling-Based Semantics for WAFs 15 D1 D2 D3 W-COM is IN IN w-defends is OUT IN a ⟺ a− = a− |OUT ∧ Arg ↓ a a ⟹ W(a− ↓ , a) < 𝕊 ⊤
- 28. FLAIRS 2021 - Extending Labelling Semantics to Weighted Argumentation Frameworks Labelling-Based Semantics for WAFs 16 D1 D2 D3 W-STB is IN IN w-defends is OUT IN UNDEC a ⟺ a− = a− |OUT ∧ Arg ↓ a a ⟹ W(a− ↓ , a) < 𝕊 ⊤ Arg ↓ = ∅
- 29. FLAIRS 2021 - Extending Labelling Semantics to Weighted Argumentation Frameworks Labelling-Based Semantics for WAFs 17 D1 D2 D3 W-GDE is IN is IN in every W-COM is OUT IN a ⟺ a a ⟹ W(a− ↓ , a) < 𝕊 ⊤
- 30. FLAIRS 2021 - Extending Labelling Semantics to Weighted Argumentation Frameworks Web Interface: www.dmi.unipg.it/conarg 18
- 31. FLAIRS 2021 - Extending Labelling Semantics to Weighted Argumentation Frameworks • Labelling Semantics for WAFs: Conclusion 19 • Di ff erent notions of w-defence • ConArg implementation ‣ w-con fl ict-free ‣ w-admissible ‣ w-complete ‣ w-stable ‣ w-preferred ‣ w-grounded
- 32. FLAIRS 2021 - Extending Labelling Semantics to Weighted Argumentation Frameworks • Di ff erentiate UNDEC with “don’t care” and “don’t know” labels ‣ Four-state labelling • De fi ne a complete labelling where empty labels are allowed • Give explicit conditions for labelling UNDEC arguments Future Work 20
- 33. Introducing a Tool for Concurrent Argumentation FLAIRS 2021 Stefano Bistarelli, Carlo Taticchi Thank you for your attention!