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)


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.


Binary Relation Semantical Representation Belief Revision Background Theory Propositional Formula 
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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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© Springer International Publishing AG 2016

Authors and Affiliations

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

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