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Explanatory Relations Revisited: Links with Credibility-Limited Revision

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Part of the Lecture Notes in Computer Science book series (LNAI,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.

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Notes

  1. 1.

    As usual we use the infix notation \(\alpha \circ \beta \) instead of \(\circ (\alpha ,\beta )\).

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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.

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Correspondence to Ramón Pino Pérez .

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León, M.V., Pino Pérez, R. (2016). Explanatory Relations Revisited: Links with Credibility-Limited Revision. In: Montes y Gómez, M., Escalante, H., Segura, A., Murillo, J. (eds) Advances in Artificial Intelligence - IBERAMIA 2016. IBERAMIA 2016. Lecture Notes in Computer Science(), vol 10022. Springer, Cham. https://doi.org/10.1007/978-3-319-47955-2_3

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  • DOI: https://doi.org/10.1007/978-3-319-47955-2_3

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