On Boolean Algebras of Conditionals and Their Logical Counterpart

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10369)

Abstract

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.

Keywords

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

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Copyright information

© 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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