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Games, Queries, and Argumentation Frameworks: Time for a Family Reunion

Research Seminar Talk (online) at KRR@UP (Uni Potsdam) on Dec 6, 2023, loosely based on a paper with the same title at the 7th Workshop on Advances in Argumentation in Artificial Intelligence (AI3)

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Games, Queries, and Argumentation Frameworks:
Time for a Family Reunion!
Bertram Ludäscher1, Shawn Bowers2, Yilin Xia1
1 School of Information Sciences, University of Illinois, Urbana-Champaign, IL, USA
2 Department of Computer Science, Gonzaga University, WA, USA
{ludaesch,yilinx2}@illinois.edu
bowers@gonzaga.edu
7th Workshop on Advances in Argumentation in Artificial Intelligence (AI3)
AIxIA 2023: 22nd International Conference of the Italian Association for Artificial Intelligence
Games, Queries, Argumentation
Outline
1. What’s this? (a puzzle)
2. Identical Twins & Some History
3. The Correspondence
4. Harvesting Time (translational research)
5. Family Reunion & Clingo clinic J
KRR@UP Seminar, Dec 6 2023 2
Games, Queries, Argumentation
What’s this? (an easy puzzle ..)
• q --> e, e, e.
• q(X,Y) :- e(X,A), e(A,B), e(B,Y).
• Input: digraph with edges e(X,Y)
• Output: binary answer relation q(X,Y)
• q(X,Y) iff there is a path of length=3 from X to Y in e/2.
KRR@UP Seminar, Dec 6 2023 3
Games, Queries, Argumentation
What’s (not) in a query?
• q(X,Y) :- e(X,A), e(A,B), e(B,Y).
• We can interpret e/2 differently => output q/2 is a different relation
• e/2 ≅ parent/2
• => q/2 ≅ great_grandparent/2
• e/2 ≅ one_hour_trail/2
• => q/2 ≅ three_hour_hike/2
KRR@UP Seminar, Dec 6 2023 4
Bonus question:
How many patterns are there for
hikes? For great-grandparents?
Games, Queries, Argumentation
What’s this? (a harder query puzzle ..)
• q(X) :- e(X,Y), not q(Y).
•Standard LP semantics:
•stratified
•stable models
•well-founded
KRR@UP Seminar, Dec 6 2023 5
Games, Queries, Argumentation
What’s this? (a harder query puzzle ..)
• q(X) :- e(X,Y), not q(Y).
• Stable models => (complement of) graph kernels of G = (V,E).
• K ⊆ V is a kernel if K is independent and dominating (aka absorbing).
• out(X) :- e(X,Y), not out(Y).
• in(X) :- not out(X).
KRR@UP Seminar, Dec 6 2023 6

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Games, Queries, and Argumentation Frameworks: Time for a Family Reunion

  • 1. 1 Games, Queries, and Argumentation Frameworks: Time for a Family Reunion! Bertram Ludäscher1, Shawn Bowers2, Yilin Xia1 1 School of Information Sciences, University of Illinois, Urbana-Champaign, IL, USA 2 Department of Computer Science, Gonzaga University, WA, USA {ludaesch,yilinx2}@illinois.edu bowers@gonzaga.edu 7th Workshop on Advances in Argumentation in Artificial Intelligence (AI3) AIxIA 2023: 22nd International Conference of the Italian Association for Artificial Intelligence
  • 2. Games, Queries, Argumentation Outline 1. What’s this? (a puzzle) 2. Identical Twins & Some History 3. The Correspondence 4. Harvesting Time (translational research) 5. Family Reunion & Clingo clinic J KRR@UP Seminar, Dec 6 2023 2
  • 3. Games, Queries, Argumentation What’s this? (an easy puzzle ..) • q --> e, e, e. • q(X,Y) :- e(X,A), e(A,B), e(B,Y). • Input: digraph with edges e(X,Y) • Output: binary answer relation q(X,Y) • q(X,Y) iff there is a path of length=3 from X to Y in e/2. KRR@UP Seminar, Dec 6 2023 3
  • 4. Games, Queries, Argumentation What’s (not) in a query? • q(X,Y) :- e(X,A), e(A,B), e(B,Y). • We can interpret e/2 differently => output q/2 is a different relation • e/2 ≅ parent/2 • => q/2 ≅ great_grandparent/2 • e/2 ≅ one_hour_trail/2 • => q/2 ≅ three_hour_hike/2 KRR@UP Seminar, Dec 6 2023 4 Bonus question: How many patterns are there for hikes? For great-grandparents?
  • 5. Games, Queries, Argumentation What’s this? (a harder query puzzle ..) • q(X) :- e(X,Y), not q(Y). •Standard LP semantics: •stratified •stable models •well-founded KRR@UP Seminar, Dec 6 2023 5
  • 6. Games, Queries, Argumentation What’s this? (a harder query puzzle ..) • q(X) :- e(X,Y), not q(Y). • Stable models => (complement of) graph kernels of G = (V,E). • K ⊆ V is a kernel if K is independent and dominating (aka absorbing). • out(X) :- e(X,Y), not out(Y). • in(X) :- not out(X). KRR@UP Seminar, Dec 6 2023 6
  • 7. Games, Queries, Argumentation What’s this? (a harder query puzzle ..) • q(X) :- e(X,Y), not q(Y). • Well-founded model => solves the game G = (Positions,Move). • win(X) :- move(X,Y), not win(Y). KRR@UP Seminar, Dec 6 2023 7
  • 8. Games, Queries, Argumentation What’s this? (a harder query puzzle ..) • q(X) :- e(X,Y), not q(Y). • Stable and Well-founded model • => solves the Argumentation Framework AF = (Args, Attacks). • defeated(X) :- attacks(Y,X), not defeated(Y). • defeated(X) :- attacked_by(X,Y), not defeated(Y). KRR@UP Seminar, Dec 6 2023 8
  • 9. Games, Queries, Argumentation Summary: One rule to rule them all … • q(X) :- e(X,Y), not q(Y). • win(X) :- move(X,Y), not win(Y). • defeated(X) :- attacked_by(X,Y), not defeated(Y). • kerC(X) :- edge(X,Y), not kerC(Y). • Has this been known in AF? • … or hiding in plain sight? KRR@UP Seminar, Dec 6 2023 9
  • 10. The AF Semantics Zoo … KRR@UP Seminar, Dec 6 2023 10
  • 11. Game Example: move(X,Y) relation a k b c l d e m g h n f 11
  • 12. Solving the Example a k b c l d e m g h n f 12
  • 13. Solving the Example a k b c l d e m g h n f 13
  • 14. Solving the Example a k b c l d e m g h n f 14
  • 15. Solving the Example a k b c l d e m g h n f 15 win(X) :- move(X,Y), not win(Y). One rule … to rule them all!
  • 16. Games, Queries, Argumentation A Claim: Stratified Datalog = FIXPOINT KRR@UP Seminar, Dec 6 2023 16
  • 17. Games, Queries, Argumentation Kolaitis’88: .. not so fast! KRR@UP Seminar, Dec 6 2023 17 17
  • 18. A question from the DB-Theory “bible” [AHV95] 18 Well-founded (WF-)Datalog queries have 3-valued models in general. Can every query Q in WF-Datalog-3 be rewritten into an equivalent Q’ in WF-Datalog-2? => Total WF-Datalog-2 =?= Partial WF-Datalog-3? Example: Can we detected draws for GAME? win(X) :- move(X,Y), not win(Y). KRR@UP Seminar, Dec 6 2023
  • 19. … answering the question! [FKL-ICDT’97] 19 All you need is GAME! (i.e., the win-move / GAME query) KRR@UP Seminar, Dec 6 2023
  • 20. … answering the question! 20 The tricky bit! Useful notion: Length of a position! All you need is DRAW-FREE GAMEs! (i.e., the win-move / GAME query, … but draws can be detected and avoided!) KRR@UP Seminar, Dec 6 2023
  • 21. Games, Queries, Argumentation Win-Move vs Argumentation Frameworks % We understand this now: • win(X) :- move(X,Y), not win(Y). % This is the mother of AF rules: • defeated(X) :- attacks(Y,X), not defeated(Y). % But they are both equivalent to this: • q(X) :- edge(X,Y), not q(Y). • GAME: q = win edge = move • AF: q = defeated edge = attacks-1 (= attacked_by) KRR@UP Seminar, Dec 6 2023 21
  • 22. The Correspondence: GAME ~ AF WF and Stable Semantics 22 KRR@UP Seminar, Dec 6 2023
  • 23. move(X,Y) 23 a b c d e f g h m k l n KRR@UP Seminar, Dec 6 2023
  • 24. attacks(Y,X) 24 a b c d e f g h m k l n KRR@UP Seminar, Dec 6 2023
  • 25. Win-Move GAME 25 a b c d e f g h m k l n KRR@UP Seminar, Dec 6 2023
  • 26. Argumentation Framework 26 a b c d e f g h m k l n KRR@UP Seminar, Dec 6 2023
  • 27. Games, Queries, Argumentation Harvesting Time: Not all edges are created equal! • Notions from games translate to AF via the natural correspondence! • Length of a position (i.e., argument) • Type of an edge (not all edges are created equal) • winning, delaying, drawing, bad KRR@UP Seminar, Dec 6 2023 27
  • 28. Games, Queries, Argumentation Harvesting Time! • Provenance of a position (i.e., argument) • ... = Explanations of the labeling • … can be computed via Regular Path Queries (RPQs): • prov(X,Y):- path(X, green(.red.green)*, Y) KRR@UP Seminar, Dec 6 2023 28 • Question: • What is the provenance of games? • Answer: • Solve the game (AF) and look! • Provenance/Explanations for free!
  • 31. Not all edges are created equal! KRR@UP Seminar, Dec 6 2023 31
  • 32. Not all edges are created equal! KRR@UP Seminar, Dec 6 2023 32
  • 33. Games, Queries, Argumentation Harvesting Time… for AF! KRR@UP Seminar, Dec 6 2023 33 W bad D bad L winning bad drawing n/a delaying n/a n/a
  • 34. Edge Types => New explanations for Argumentation Frameworks ... !? 34 Applying this to AF (coming from GAME and provenance) seems new… KRR@UP Seminar, Dec 6 2023
  • 35. Games, Queries, Argumentation Finally: Computing WFS with Clingo • How do you compute the well-founded semantics with an ASP system? • … should be easy … KRR@UP Seminar, Dec 6 2023 35
  • 36. Games, Queries, Argumentation Statelog to the rescue … A locally (state-)stratified program will do. KRR@UP Seminar, Dec 6 2023 36
  • 37. Games, Queries, Argumentation Summary: Time for a Family Reunion! 1. Identical LP Twins (triplets) • Game- & DB-Theory: win-move • Argumentation: defeated-attacked_by • Graph Theory: kernels • Semantics: Well-founded, Stable, … 2. Harvesting Time (translational research) • Not all edges are created equal! (types) • Length of positions/arguments • Decomposition Theorem (Fraenkel, Flum) • Provenance & Explainability KRR@UP Seminar, Dec 6 2023 37 Join the reunion!