Skip to main content

\( ASPIC ^?\) and the Postulates of Non-interference and Crash-Resistance

  • Conference paper
  • First Online:
Intelligent Systems (BRACIS 2021)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 13073))

Included in the following conference series:

  • 582 Accesses


We introduce an interrogation mark ? in \( ASPIC ^+\) languages as a plausibility operator to enhance any defeasible conclusion does not have the same status as an irrefutable one. The resulting framework, dubbed \( ASPIC ^?\), is tailored to make a distinction between strong inconsistencies and weak inconsistencies. The aim is to avoid the former and to tolerate the latter. This means the extensions obtained from the \( ASPIC ^?\) framework are free of strong conflicts, but tolerant to weak conflicts. Then, in the current study, we show \( ASPIC ^?\) satisfy reasonable properties. In particular, we focus on the property that a conflict between two arguments should not interfere with the acceptability of other unrelated arguments. With this purpose in mind, we prove under which conditions the important principles of Non-interference and Crash-Resistance hold in \( ASPIC ^?\).

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

Access this chapter

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
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

Similar content being viewed by others


  1. Carnielli, W., Marcos, J.: A taxonomy of C-systems. In: Paraconsistency, pp. 24–117. CRC Press (2002)

    Google Scholar 

  2. Pequeno, T., Buchsbaum, A.: The logic of epistemic inconsistency. In: Proceedings of the Second International Conference on Principles of Knowledge Representation and Reasoning, pp. 453–460 (1991)

    Google Scholar 

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

    Article  MathSciNet  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  5. Caminada, M., Modgil, S., Oren, N.: Preferences and unrestricted rebut. Computational Models of Argument (2014)

    Google Scholar 

  6. Grooters, D., Prakken, H.: Combining paraconsistent logic with argumentation. In: COMMA, pp. 301–312 (2014)

    Google Scholar 

  7. Wu, Y.: Between argument and conclusion-argument-based approaches to discussion, inference and uncertainty. Ph.D. thesis, University of Luxembourg (2012)

    Google Scholar 

  8. Wu, Y., Podlaszewski, M.: Implementing crash-resistance and non-interference in logic-based argumentation. J. Logic Comput. 25(2), 303–333 (2015)

    Article  MathSciNet  Google Scholar 

  9. Rescher, N., Manor, R.: On inference from inconsistent premisses. Theory Decis. 1(2), 179–217 (1970)

    Article  Google Scholar 

  10. Caminada, M.: Semi-stable semantics. OMMA 144, 121–130 (2006)

    MathSciNet  Google Scholar 

  11. Dung, P.: 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 

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

    Article  Google Scholar 

  13. Damásio, C., Moniz Pereira, L.: A survey of paraconsistent semantics for logic programs. In: Besnard, P., Hunter, A. (eds.) Reasoning with Actual and Potential Contradictions. Handbook of Defeasible Reasoning and Uncertainty Management Systems, vol. 2, pp. 241–320. Springer, Cham (1998).

Download references

Author information

Authors and Affiliations


Corresponding author

Correspondence to Rafael Silva .

Editor information

Editors and Affiliations

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

Silva, R., Alcântara, J. (2021). \( ASPIC ^?\) and the Postulates of Non-interference and Crash-Resistance. In: Britto, A., Valdivia Delgado, K. (eds) Intelligent Systems. BRACIS 2021. Lecture Notes in Computer Science(), vol 13073. Springer, Cham.

Download citation

  • DOI:

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-91701-2

  • Online ISBN: 978-3-030-91702-9

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics