Advertisement

Explanatory Relations Revisited: Links with Credibility-Limited Revision

  • María Victoria León
  • Ramón Pino PérezEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10022)

Abstract

We study binary relations \(\rhd \) over propositional formulas built over a finite set of variables. The meaning of \(\alpha \rhd \gamma \) is that \(\gamma \) is a preferred explanation of the observation \(\alpha \). These relations are called Explanatory or abductive relations. We find two important families of abductive relations characterized by his axiomatic behavior: the ordered explanatory relations and the weakly reflexive explanatory relations. We show that both families have tight links with the framework of Credibility limited revision. These relationships allow to establish semantical representations for each family. An important corollary of our representations results is that our axiomatizations allow us to overcome the background theory present in most axiomatizations of abduction.

Keywords

Binary Relation Semantical Representation Belief Revision Background Theory Propositional Formula 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgements

Thanks to the anonymous referees for their helpful remarks. The second author was partially supported by the research project CDCHT-ULA N\(^\circ \) C-1451-07-05- A.

References

  1. 1.
    Alchourrón, C.E.: Detachment and defeasibility in deontic logic. Stud. Logica. 51, 5–18 (1996)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Alchourrón, C.E., Gärdenfors, P., Makinson, D.: On the logic of theory change: partial meet contraction and revision functions. J. Symbolic Logic 50, 510–530 (1985)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Bloch, I., Pino-Pérez, R., Uzcátegui, C.: Explanatory relations based on mathematical morphology. In: Benferhat, S., Besnard, P. (eds.) ECSQARU 2001. LNCS (LNAI), vol. 2143, pp. 736–747. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  4. 4.
    Booth, R., Fermé, E., Konieczny, S., Pino Pérez, R.: Credibility limited revision operators in propositional logic. In: Proceedings of the Thirteenth International Conference on Principles of Knowledge Representation And Reasoning, pp. 116–125 (2012)Google Scholar
  5. 5.
    Boutilier, C., Becher, V.: Abduction as belief revision. Artif. Intell. 77, 43–94 (1995)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Mayer, M.C., Pirri, F.: Abduction is not deduction-in-reverse. J. IGPL 4(1), 1–14 (1996)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Falappa, M.A., Kern-Isberner, G., Simari, G.R.: Explanations, belief revision and defeasible reasoning. Artif. Intell. 143, 1–28 (2002)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Fermé, E., Rodríguez, R.: DFT and belief revision. Análisis Filosófico XXVII(2), 373–393 (2006)Google Scholar
  9. 9.
    Flach, P.A.: Rationality postulates for induction. In: Shoam, Y. (ed.) Proceedings of the Sixth Conference of Theoretical Aspects of Rationality and Knowledge (TARK-96), pp. 267–281 (1996)Google Scholar
  10. 10.
    Flach, P.A.: Logical characteristics of inductive learning. In: Gabbay, D.M., Kruse, R. (eds.) Abductive Reasoning and Learning, pp. 155–196 (2000)Google Scholar
  11. 11.
    Hansson, S.O., Fermé, E.L., Cantwell, J., Falappa, M.A.: Credibility limited revision. J. Symbolic Logic 66, 1581–1596 (2001)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Katsuno, H., Mendelzon, A.: Propositional knowledge base revision and minimal change. Artif. Intell. 52, 263–294 (1991)MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Levesque, H.J.: A knowledge level account of abduction. In: Proceedings of the Eleventh International Joint Conference on Artificial Intelligence, Detroit, pp. 1061–1067 (1989)Google Scholar
  14. 14.
    Pagnucco, M.: The Role of Abductive Reasoning Within the Process of Belief Revision. Ph.D. thesis, Department of Computer Science, University of Sydney, February 1996Google Scholar
  15. 15.
    Pino Pérez, R., Uzcátegui, C.: Jumping to explanations vs jumping to conclusions. Artif. Intell. 111(2), 131–169 (1999)CrossRefzbMATHGoogle Scholar
  16. 16.
    Pino Pérez, R., Uzcátegui, C.: Preferences and explanations. Artif. Intell. 149(1), 1–30 (2003)MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    Walliser, B., Zwirn, D., Zwirn, H.: Abductive logic in a belief revision framework. J. Logic Lang. Inf. 14, 87–117 (2005)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer International Publishing AG 2016

Authors and Affiliations

  1. 1.Departamento de Matemáticas, Facultad de cienciasUniversidad de Los AndesMéridaVenezuela

Personalised recommendations