On Boolean Algebras of Conditionals and Their Logical Counterpart

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. © Springer International Publishing AG 2017.Flaminio and Godo acknowledge partial support by the Spanish FEDER/MINECO project TIN2015-71799- C2-1-P.Peer Reviewe