Skip to main content
SpringerLink
Log in

Computing Defeasible Meta-logic

  • 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

The use of meta-rules, i.e., rules whose content includes other rules, has been advocated to model policies and the notion of power in legal reasoning, where an agent has the power to create new norms affecting other agents. The use of Defeasible Logic (DL) to model meta-rules in the application area we just alluded to has been investigated, but not from a computational viewpoint. Our aim is to fill this gap by introducing a variant of DL, Defeasible Meta-Logic, to represent defeasible meta-theories, by proposing efficient algorithms to compute the (meta-)extensions of such theories, and by proving their computational complexity.

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.

    The strong negation principle applies the function that simplifies a formula by moving all negations to an inner most position in the resulting formula, and replaces the positive tags with the respective negative tags, and the other way around see [15].

References

  1. Antoniou, G., Billington, D., Governatori, G., Maher, M.J.: Representation results for defeasible logic. ACM Trans. Comput. Log. 2(2), 255–287 (2001). https://doi.org/10.1145/371316.371517

    Article  MathSciNet  MATH  Google Scholar 

  2. Azab, K., Habel, A.: High-level programs and program conditions. In: Ehrig, H., Heckel, R., Rozenberg, G., Taentzer, G. (eds.) ICGT 2008. LNCS, vol. 5214, pp. 211–225. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-87405-8_15

    Chapter  Google Scholar 

  3. Basin, D., Clavel, M., Meseguer, J.: Reflective metalogical frameworks. ACM Trans. Comput. Logic 5(3), 528–576 (2004). https://doi.org/10.1145/1013560.1013566

    Article  MathSciNet  MATH  Google Scholar 

  4. Cristani, M., Olivieri, F., Rotolo, A.: Changes to temporary norms. In: Keppens, J., Governatori, G. (eds.) ICAIL 2017 pp. 39–48. ACM. https://doi.org/10.1145/3086512.3086517

  5. Dastani, M., Governatori, G., Rotolo, A., Song, I., van der Torre, L.: Contextual agent deliberation in defeasible logic. In: Ghose, A., Governatori, G., Sadananda, R. (eds.) PRIMA 2007. LNCS (LNAI), vol. 5044, pp. 98–109. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-01639-4_9

    Chapter  Google Scholar 

  6. Dupin De Saint-Cyr, F., Bisquert, P., Cayrol, C., Lagasquie-Schiex, M.C.: Argumentation update in YALLA (yet another logic language for argumentation). Int. J. Approx. Reason. 75, 57–92 (2016). https://doi.org/10.1016/j.ijar.2016.04.003

  7. Dyoub, A., Costantini, S., De Gasperis, G.: Answer set programming and agents. Knowl. Eng. Rev. 33(1) (2018). https://doi.org/10.1017/S0269888918000164

  8. Eiter, T., Faber, W., Leone, N., Pfeifer, G.: Computing preferred answer sets by meta-interpretation in answer set programming. Theory Pract. Logic Program. 3(4–5), 463–498 (2003). https://doi.org/10.1017/S1471068403001753

    Article  MathSciNet  MATH  Google Scholar 

  9. Gabbay, D.M., Giordano, L., Martelli, A., Olivetti, N.: A language for handling hypothetical updates and inconsistency. Log. J. IGPL 4(3), 385–416 (1996). https://doi.org/10.1093/jigpal/4.3.385

  10. Gelati, J., Governatori, G., Rotolo, A., Sartor, G.: Normative autonomy and normative co-ordination: declarative power, representation, and mandate. Artif. Intell. Law 12(1–2), 53–81 (2004)

    Article  Google Scholar 

  11. Ghidini, C., Giunchiglia, F.: Local models semantics, or contextual reasoning = locality + compatibility. Artif. Intell. 127(2), 221–259 (2001). https://doi.org/10.1016/S0004-3702(01)00064-9

    Article  MathSciNet  MATH  Google Scholar 

  12. Governatori, G., Olivieri, F., Rotolo, A., Scannapieco, S.: Computing strong and weak permissions in defeasible logic. J. Philos. Logic 42(6), 799–829 (2013). https://doi.org/10.1007/s10992-013-9295-1

    Article  MathSciNet  MATH  Google Scholar 

  13. Governatori, G., Olivieri, F., Scannapieco, S., Cristani, M.: Designing for compliance: norms and goals. In: Olken, F., Palmirani, M., Sottara, D. (eds.) RuleML 2011. LNCS, vol. 7018, pp. 282–297. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-24908-2_29

    Chapter  Google Scholar 

  14. Governatori, G., Olivieri, F., Scannapieco, S., Rotolo, A., Cristani, M.: The rationale behind the concept of goal. Theory Pract. Log. Program. 16(3), 296–324 (2016). https://doi.org/10.1017/S1471068416000053

    Article  MathSciNet  MATH  Google Scholar 

  15. Governatori, G., Padmanabhan, V., Rotolo, A., Sattar, A.: A defeasible logic for modelling policy-based intentions and motivational attitudes. Log. J. IGPL 17(3), 227–265 (2009). https://doi.org/10.1093/jigpal/jzp006

    Article  MathSciNet  MATH  Google Scholar 

  16. Governatori, G., Rotolo, A.: Changing legal systems: legal abrogations and annulments in defeasible logic. Log. J. IGPL 18(1), 157–194 (2010)

    Article  MathSciNet  Google Scholar 

  17. Greco, S., Leone, N., Scarcello, F.: Datalog with nested rules. In: Dix, J., Pereira, L.M., Przymusinski, T.C. (eds.) LPKR 1997. LNCS, vol. 1471, pp. 52–65. Springer, Heidelberg (1998). https://doi.org/10.1007/BFb0054789

    Chapter  Google Scholar 

  18. Jones, A.J.I., Sergot, M.J.: A formal characterisation of institutionalised power. Log. J. IGPL 4(3), 427–443 (1996). https://doi.org/10.1093/jigpal/4.3.427

    Article  MathSciNet  MATH  Google Scholar 

  19. Kravari, K., Bassiliades, N.: A survey of agent platforms. J. Artif. Soc. Soc. Simul. 18(1),  11 (2015). https://doi.org/10.18564/jasss.2661

  20. Lifschitz, V., Tang, L.R., Turner, H.: Nested expressions in logic programs. Ann. Math. Artif. Intell. 25(3), 369–389 (1999). https://doi.org/10.1023/A:1018978005636

    Article  MathSciNet  MATH  Google Scholar 

  21. Lloyd, J.W., Topor, R.W.: Making prolog more expressive. J. Logic Program. 1(3), 225–240 (1984). https://doi.org/10.1016/0743-1066(84)90011-6

    Article  MathSciNet  MATH  Google Scholar 

  22. Makinson, D., Van Der Torre, L.: Input/output logics. J. Philos. Logic 29(4), 383–408 (2000)

    Article  MathSciNet  Google Scholar 

  23. Modgil, S., Bench-Capon, T.: Metalevel argumentation. J. Logic Comput. 21(6), 959–1003 (2011). https://doi.org/10.1093/logcom/exq054

    Article  MathSciNet  MATH  Google Scholar 

  24. Olivieri, F., Cristani, M., Governatori, G.: Compliant business processes with exclusive choices from agent specification. In: Chen, Q., Torroni, P., Villata, S., Hsu, J., Omicini, A. (eds.) PRIMA 2015. LNCS (LNAI), vol. 9387, pp. 603–612. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-25524-8_43

    Chapter  Google Scholar 

  25. Olivieri, F., Governatori, G., Scannapieco, S., Cristani, M.: Compliant business process design by declarative specifications. In: Boella, G., Elkind, E., Savarimuthu, B.T.R., Dignum, F., Purvis, M.K. (eds.) PRIMA 2013. LNCS (LNAI), vol. 8291, pp. 213–228. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-44927-7_15

    Chapter  Google Scholar 

  26. Sartor, G.: Legal Reasoning: A Cognitive Approach to the Law. Springer (2005)

    Google Scholar 

  27. Song, I., Governatori, G.: Nested rules in defeasible logic. In: Adi, A., Stoutenburg, S., Tabet, S. (eds.) RuleML 2005. LNCS, vol. 3791, pp. 204–208. Springer, Heidelberg (2005). https://doi.org/10.1007/11580072_18

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute for Integrated and Intelligent Systems, Griffith University, Nathan, QLD, 4111, Australia

    Francesco Olivieri & Abdul Sattar

  2. Data61, CSIRO, Dutton Park, QLD, 4102, Australia

    Guido Governatori

  3. University of Verona, 37136, Verona, Italy

    Matteo Cristani

Authors
  1. Francesco Olivieri
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Guido Governatori
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Matteo Cristani
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Abdul Sattar
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Matteo Cristani .

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

Olivieri, F., Governatori, G., Cristani, M., Sattar, A. (2021). Computing Defeasible Meta-logic. 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_6

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-75775-5_6

  • 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