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A Discussion Game for Grounded Semantics

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Theory and Applications of Formal Argumentation (TAFA 2015)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 9524))

Abstract

We introduce an argument-based discussion game where the ability to win the game for a particular argument coincides with the argument being in the grounded extension. Our game differs from previous work in that (i) the number of moves is linear (instead of exponential) w.r.t. the strongly admissible set that the game is constructing, (ii) winning the game does not rely on cooperation from the other player (that is, the game is winning strategy based), (iii) a single game won by the proponent is sufficient to show grounded membership, and (iv) the game has a number of properties that make it more in line with natural discussion.

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Notes

  1. 1.

    We say that there is a \( HTB \)-\( CB \) repeat iff \(\exists i,j \in \{1 \ldots n\} \exists A \in Ar : (M_i = HTB (A) \vee M_i = CB (A)) \wedge (M_j = HTB (A) \vee M_j = CB (A)) \wedge i \ne j\).

  2. 2.

    A move \( CONCEDE (B)\) is applicable iff the discussion contains a move \( HTB (A)\) and for every attacker A of B the discussion contains a move \( RETRACT (B)\), and the discussion does not already contain a move \( CONCEDE (B)\). A move \( RETRACT (B)\) is applicable iff the discussion contains a move \( CB (B)\) and there is an attacker A of B such that the discussion contains a move \( CONCEDE (A)\), and the discussion does not already contain a move \( RETRACT (B)\).

  3. 3.

    We write “a lowest number strategy” instead of “the lowest number strategy” as a lowest number strategy might not be unique due to different lowest numbered \(\mathtt {in}\)-labelled arguments being applicable at a specific point. In that case it suffices to pick an arbitrary one.

  4. 4.

    What we call an SGG game is called a “line of dispute” in [19].

  5. 5.

    A similar observation can be made for other tree-based proof procedures [11, 14].

  6. 6.

    As each move contains a single argument, this means the “communication complexity” (the total number of arguments that needs to be communicated) is also linear. This contrasts with the computational complexity of playing the game, which is polynomial (\(O(n^3)\), where n is the number of arguments) due to the fact that selecting the next move can have \(O(n^2)\) complexity (see [6] for details). This is still less than when applying Standard Grounded Game, whose overall complexity would be exponential (even if each move could be selected in just one step) due to the requirement of a winning strategy, which as we have seen can be exponential in size.

  7. 7.

    A discussion is won by P iff at the end of the game O is committed that the argument the discussion started with is labelled \(\mathtt {in}\).

  8. 8.

    That is, if one regards all arguments where O does not have any commitments to be labelled \(\mathtt {undec}\).

  9. 9.

    For instance, if a conclusion is considered justified in aspic+ [21, 26], does this imply the conclusion is also true?.

References

  1. Baroni, P., Giacomin, M.: On principle-based evaluation of extension-based argumentation semantics. Artif. Intell. 171(10–15), 675–700 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  2. Bondarenko, A., Dung, P.M., Kowalski, R.A., Toni, F.: An abstract, argumentation-theoretic approach to default reasoning. Artif. Intell. 93, 63–101 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  3. Caminada, M.W.A.: For the sake of the Argument. Explorations into argument-based reasoning. Doctoral dissertation Free University Amsterdam (2004)

    Google Scholar 

  4. Caminada, M.W.A.: A formal account of socratic-style argumentation. J. Appl. Log. 6(1), 109–132 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  5. Caminada, M.W.A.: Strong admissibility revisited. In: Parsons, S., Oren, N., Reed, C., Cerutti, F. (eds.) Computational Models of Argument; Proceedings of COMMA 2014, pp. 197–208. IOS Press (2014)

    Google Scholar 

  6. Caminada, M.W.A.: A discussion protocol for grounded semantics (proofs). Technical report, University of Aberdeen (2015)

    Google Scholar 

  7. Caminada, M.W.A., Dvořák, W., Vesic, S.: Preferred semantics as socratic discussion. J. Log. Comput. (2014). (in print)

    Google Scholar 

  8. Caminada, M.W.A., Gabbay, D.M.: A logical account of formal argumentation. Stud. Logica 93(2–3), 109–145 (2009). Special issue: new ideas in argumentation theory

    Article  MATH  MathSciNet  Google Scholar 

  9. Caminada, M.W.A., Podlaszewski, M.: Grounded semantics as persuasion dialogue. In: Verheij, B., Szeider, S., Woltran, S. (eds.) Computational Models of Argument - Proceedings of COMMA 2012, pp. 478–485 (2012)

    Google Scholar 

  10. Caminada, M.W.A., Wu, Y.: An argument game of stable semantics. Log. J. IGPL 17(1), 77–90 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  11. Dung, P.M., Mancarella, P., Toni, F.: Computing ideal sceptical argumentation. Artif. Intell. 171(10–15), 642–674 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  12. Dung, P.M.: On the acceptability of arguments and its fundamental role in nonmonotonic reasoning, logic programming and \(n\)-person games. Artif. Intell. 77, 321–357 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  13. Dung, P.M., Kowalski, R.A., Toni, F.: Assumption-based argumentation. In: Simari, G., Rahwan, I. (eds.) Argumentation in Artificial Intelligence, pp. 199–218. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  14. Fan, X., Toni, F.: A general framework for sound assumption-based argumentation dialogues. Artif. Intell. 216, 20–54 (2014)

    Article  MATH  MathSciNet  Google Scholar 

  15. Gorogiannis, N., Hunter, A.: Instantiating abstract argumentation with classical logic arguments: Postulates and properties. Artif. Intell. 175(9–10), 1479–1497 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  16. Mackenzie, J.D.: Question-begging in non-cumulative systems. J. Philos. Log. 8, 117–133 (1979)

    Article  MATH  MathSciNet  Google Scholar 

  17. Mackenzie, J.D.: Four dialogue systems. Stud. Logica 51, 567–583 (1990)

    Article  MathSciNet  Google Scholar 

  18. Modgil, S.: Reasoning about preferences in argumentation frameworks. Artif. Intell. 173, 901–1040 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  19. Modgil, S., Caminada, M.W.A.: Proof theories and algorithms for abstract argumentation frameworks. In: Rahwan, I., Simari, G.R. (eds.) Argumentation in Artificial Intelligence, pp. 105–129. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  20. Modgil, S., Prakken, H.: A general account of argumentation with preferences. Artif. Intell. 195, 361–397 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  21. Modgil, S., Prakken, H.: The ASPIC+ framework for structured argumentation: a tutorial. Argum. Comput. 5, 31–62 (2014). Special Issue: Tutorials on Structured Argumentation

    Article  Google Scholar 

  22. Parsons, S., Wooldridge, M., Amgoud, L.: Properties and complexity of formal inter-agent dialogues. J. Log. Comput. 13(3), 347–376 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  23. Podlaszewski, M., Wu, Y., Caminada, M.: An implementation of basic argumentation components. In: The 10th International Conference on Autonomous Agents and Multiagent Systems, vol. 3, pp. 1307–1308 (2011)

    Google Scholar 

  24. Prakken, H.: Coherence and flexibility in dialogue games for argumentation. J. Log. Comput. 15(6), 1009–1040 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  25. Prakken, H.: Formal systems for persuasion dialogue. Knowl. Eng. Rev. 21, 163–188 (2006)

    Article  Google Scholar 

  26. Prakken, H.: An abstract framework for argumentation with structured arguments. Argum. Comput. 1(2), 93–124 (2010)

    Article  Google Scholar 

  27. Prakken, H., Sartor, G.: Argument-based extended logic programming with defeasible priorities. J. Appl. Non-Classical Log. 7, 25–75 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  28. Schulz, C.: Graphical representation of assumption-based argumentation. In: Proceedings of the 29th AAAI Conference on Artificial Intelligence, pp. 4204–4205 (2015)

    Google Scholar 

  29. Schulz, C., Toni, F.: Logic programming in assumption-based argumentation revisited - semantics and graphical representation. In: Proceedings of the 29th AAAI Conference on Artificial Intelligence, pp. 1569–1575 (2015)

    Google Scholar 

  30. Toni, F.: A tutorial on assumption-based argumentation. Argum. Comput. 5, 89–117 (2014). Special Issue: Tutorials on Structured Argumentation

    Article  Google Scholar 

  31. Walton, D.N., Krabbe, E.C.W.: Commitment in Dialogue: Basic Concepts of Interpersonal Reasoning. SUNY Series in Logic and Language. State University of New York Press, Albany (1995)

    Google Scholar 

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Acknowledgements

This work has been supported by the Engineering and Physical Sciences Research Council (EPSRC, UK), grant ref. EP/J012084/1 (SAsSy project).

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Authors and Affiliations

  1. University of Aberdeen, Aberdeen, Scotland, UK

    Martin Caminada

  2. Cardiff University, Cardiff, Wales, UK

    Martin Caminada

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  1. Martin Caminada
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Correspondence to Martin Caminada .

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Editors and Affiliations

  1. King's College London, London, United Kingdom

    Elizabeth Black

  2. Strand Building;Strand Campus, King's College London, London, United Kingdom

    Sanjay Modgil

  3. Department of Computing Science, University of Aberdeen, Aberdeen, United Kingdom

    Nir Oren

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Caminada, M. (2015). A Discussion Game for Grounded Semantics. In: Black, E., Modgil, S., Oren, N. (eds) Theory and Applications of Formal Argumentation. TAFA 2015. Lecture Notes in Computer Science(), vol 9524. Springer, Cham. https://doi.org/10.1007/978-3-319-28460-6_4

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  • DOI: https://doi.org/10.1007/978-3-319-28460-6_4

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