Skip to main content
SpringerLink
Log in

Probabilistic Argumentation: An Approach Based on Conditional Probability –A Preliminary Report–

  • Conference paper
  • First Online:
Logics in Artificial Intelligence (JELIA 2021)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 12678))

Included in the following conference series:

Abstract

A basic form of an instantiated argument is as a pair (support, conclusion) standing for a conditional relation ‘if support then conclusion’. When this relation is not fully conclusive, a natural choice is to model the argument strength with the conditional probability of the conclusion given the support. In this paper, using a very simple language with conditionals, we explore a framework for probabilistic logic-based argumentation based on an extensive use of conditional probability, where uncertain and possibly inconsistent domain knowledge about a given scenario is represented as a set of defeasible rules quantified with conditional probabilities. We then discuss corresponding notions of attack and defeat relations between arguments, providing a basis for appropriate acceptability semantics, e.g. based on extensions or on DeLP-style dialogical trees.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 79.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 99.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    Since there is no place to confusion, we will use the same symbol P to denote the probability distribution over \(\varOmega \) and its associated probability over Fm.

  2. 2.

    According to \(\vdash \).

  3. 3.

    Standing for factual or conditioned arguments.

References

  1. Bamber, D., Goodman, I.R., Nguyen, H.T.: Robust reasoning with rules that have exceptions: from second-order probability to argumentation via upper envelopes of probability and possibility plus directed graphs. Ann. Math. Artif. Intell. 45, 83–171 (2005)

    Article  MathSciNet  Google Scholar 

  2. Bodanza, G.A., Alessio, C.A.: Rethinking specificity in defeasible reasoning and its effect in argument reinstatement. Inf. Comput. 255, 287–310 (2017)

    Article  MathSciNet  Google Scholar 

  3. Cerutti, F., Thimm, M.: A general approach to reasoning with probabilities. Int. J. Approximate Reasoning 111, 35–50 (2019)

    Article  MathSciNet  Google Scholar 

  4. Dung, P.M.: On the acceptability of arguments and its fundamental role in nonmonotonic reasoning, logic programming, and n-person games. Artif. Intell. 77(2), 321–357 (1995)

    Article  MathSciNet  Google Scholar 

  5. P. M. Dung and P. M. Thang. Towards probabilistic argumentation for jury-based dispute resolution. In: Baroni, P., Cerutti, F., Giacomin, M., Simari, G.R. (eds.) Proceedings of COMMA 2010, volume 216 of Frontiers in Artificial Intelligence and Applications, pp. 171–182. IOS Press Inc. (2010)

    Google Scholar 

  6. Flaminio, T., Godo, L., Hosni, H.: Boolean algebras of conditionals, probability and logic. Artif. Intell. 286, 103347 (2020)

    Article  MathSciNet  Google Scholar 

  7. Garcia, A., Simari, G.: Defeasible logic programming: an argumentative approach. Theory Pract. Logic Program. 4(1–2), 95–138 (2004)

    Article  MathSciNet  Google Scholar 

  8. Garcia, A., Simari, G.: Argumentation based on logic programming. In: Baroni, P., Gabbay, D.M., Giacomin, M., van der Torre, L. (eds.) Handbook of Formal Argumentation, pp. 409–437. College Publications (2018)

    Google Scholar 

  9. Gilio, A., Pfeifer, N., Sanfilippo, G.: Transitivity in coherence-based probability logic. J. Appl. Logic 14, 46–64 (2016)

    Article  MathSciNet  Google Scholar 

  10. Hunter, A.: A probabilistic approach to modelling uncertain logical arguments. Int. J. Approximate Reasoning 54(1), 47–81 (2013)

    Article  MathSciNet  Google Scholar 

  11. Hunter, A.: Probabilistic qualification of attack in abstract argumentation. IJAR 55(2), 607–638 (2014)

    MathSciNet  MATH  Google Scholar 

  12. Hunter, A., Thimm, M.: On partial information and contradictions in probabilistic abstract argumentation. In: Baral, C., et al. (eds.) Proceedings of KR 2016, pp. 53–62. AAAI Press (2016)

    Google Scholar 

  13. Hunter, A., Thimm, M.: Probabilistic reasoning with abstract argumentation frameworks. J. Artif. Intell. Res. 59, 565–611 (2017)

    Article  MathSciNet  Google Scholar 

  14. Kern-Isberner, G. (ed.): Conditionals in Nonmonotonic Reasoning and Belief Revision. LNCS (LNAI), vol. 2087. Springer, Heidelberg (2001). https://doi.org/10.1007/3-540-44600-1

    Book  MATH  Google Scholar 

  15. Li, H., Oren, N., Norman, T.J.: Probabilistic argumentation frameworks. In: Modgil, S., Oren, N., Toni, F. (eds.) TAFA 2011. LNCS (LNAI), vol. 7132, pp. 1–16. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-29184-5_1

    Chapter  Google Scholar 

  16. Modgil, S., Prakken, H.: Abstract rule-based argumentation. In: Baroni, P., Gabbay, D.M., Giacomin, M., van der Torre, L. (eds.) Handbook of Formal Argumentation, pp. 409–437. College Publications (2018)

    Google Scholar 

  17. Pollock, J.L.: Justification and defeat. Artif. Intell. 67, 377–408 (1994)

    Article  MathSciNet  Google Scholar 

  18. Pollock, J.L.: Cognitive Carpentry. A Blueprint for How to Build a Person. MIT Press, Cambridge (1995)

    Book  Google Scholar 

  19. Prakken, H.: Historical overview of formal argumentation. In: Baroni, P., Gabbay, D., Giacomin, M., van der Torre, L. (eds.) Handbook of Formal Argumentation, vol. 1, pp. 73–141. College Publications (2018)

    Google Scholar 

  20. Prakken, H.: Probabilistic strength of arguments with structure. In: Thielscher, M., Toni, F., Wolter, F. et al. (eds.) Proceedings of KR 2018, pp. 158–167. AAAI Press (2018)

    Google Scholar 

  21. Talbott, W.: Bayesian epistemology. In: Zalta, E.N. (eds.) The Stanford Encyclopedia of Philosophy. Metaphysics Research Lab, Stanford University (2016)

    Google Scholar 

  22. Thimm, M., Kern-Isberner, G., Fisseler, J.: Relational probabilistic conditional reasoning at maximum entropy. In: Liu, W. (ed.) ECSQARU 2011. LNCS (LNAI), vol. 6717, pp. 447–458. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-22152-1_38

    Chapter  MATH  Google Scholar 

  23. Timmer, S., Meyer, J.J.C., Prakken, H., Renooij, S., Verheij, B.: A two-phase method for extracting explanatory arguments from Bayesian networks. Int. J. Approximate Reasoning 80, 475–494 (2017)

    Article  MathSciNet  Google Scholar 

  24. Toni, F.: A tutorial on assumption-based argumentation. Argument Comput. 5(1), 89–117 (2014)

    Article  Google Scholar 

  25. Verheij, B.: Jumping to conclusions: a logico-probabilistic foundation for defeasible rule-based arguments. In: del Cerro, L.F., Herzig, A., Mengin, J. (eds.) JELIA 2012. LNCS (LNAI), vol. 7519, pp. 411–423. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-33353-8_32

    Chapter  Google Scholar 

  26. Wilhelm, M., Kern-Isberner, G., Ecke, A.: Propositional probabilistic reasoning at maximum entropy modulo theories. In: Markov, Z., Russell, I. (eds.) Proceedings of the 29th International Florida Artificial Intelligence Research Society Conference, FLAIRS 2016, pp. 690–694. AAAI Press (2016)

    Google Scholar 

Download references

Acknowledgments

The authors acknowledge partial support by the Spanish projects TIN2015-71799-C2-1-P and PID2019-111544GB-C21.

Author information

Authors and Affiliations

  1. Universitat Autònoma de Barcelona and Barcelona Graduate School of Mathematics, Bellaterra, Spain

    Pilar Dellunde

  2. Artificial Intelligence Research Institute (IIIA-CSIC), Campus de la UAB, 08193, Bellaterra, Barcelona, Spain

    Pilar Dellunde, Lluís Godo & Amanda Vidal

Authors
  1. Pilar Dellunde
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Lluís Godo
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Amanda Vidal
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Pilar Dellunde .

Editor information

Editors and Affiliations

  1. University of Klagenfurt, Klagenfurt, Austria

    Wolfgang Faber

  2. University of Klagenfurt, Klagenfurt, Austria

    Gerhard Friedrich

  3. University of Klagenfurt, Klagenfurt, Austria

    Martin Gebser

  4. University of Klagenfurt, Klagenfurt, Austria

    Michael Morak

Rights and permissions

Reprints and permissions

Copyright information

© 2021 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Dellunde, P., Godo, L., Vidal, A. (2021). Probabilistic Argumentation: An Approach Based on Conditional Probability –A Preliminary Report–. In: Faber, W., Friedrich, G., Gebser, M., Morak, M. (eds) Logics in Artificial Intelligence. JELIA 2021. Lecture Notes in Computer Science(), vol 12678. Springer, Cham. https://doi.org/10.1007/978-3-030-75775-5_3

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-75775-5_3

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-75774-8

  • Online ISBN: 978-3-030-75775-5

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation