On Boolean Algebras of Conditionals and Their Logical Counterpart

  • Tommaso Flaminio
  • Lluis GodoEmail author
  • Hykel Hosni
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10369)


This paper sheds a novel light on the longstanding problem of investigating the logic of conditional events. Building on the framework of Boolean algebras of conditionals previously introduced by the authors, we make two main new contributions. First, we fully characterise the atomic structure of these algebras of conditionals. Second, we introduce the logic of Boolean conditionals (LBC) and prove its completeness with respect to the natural semantics induced by the structural properties of the atoms in a conditional algebra as described in the first part. In addition we outline the close connection of LBC with preferential consequence relations, arguably one of the most appreciated systems of non-monotonic reasoning.


Conditionals events Uncertain reasoning Boolean algebra of conditionals Non-monotonic reasoning 



We are thankful to the anonymous reviewers. Flaminio and Godo acknowledge partial support by the Spanish FEDER/MINECO project TIN2015-71799-C2-1-P.


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© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Dipartimento di Scienze Teoriche e ApplicateUniversità dell’InsubriaVareseItaly
  2. 2.Artificial Intelligence Research Institute (IIIA - CSIC)BellaterraSpain
  3. 3.Department of PhilosophyUniversity of MilanMilanoItaly

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