In the present seminar, we present a class of algebras obtained by adding a normal modality to Boolean algebras for conditionals so as to provide an algebraic setting for the logic C1 for counterfactual conditionals, axiomatized by Lewis. These modal algebras, that we name “Lewis algebras”, are particular Boolean algebras with operators and, as such, allow a dual relational counterpart that will be called Lewis frames. The main results of this paper show that: (1) Lewis algebras and Lewis frames provide a sound semantics for Lewis logic C1; (2) Lewis’ original sphere semantics for counterfactuals can actually be defined from Lewis frames, and hence, from Lewis algebras. Finally, we will present a new logic for counterfactuals that, taking inspiration from the definition of Lewis algebras, is obtained as a modal expansion of the recently introduced logic LBC to reason about Boolean conditionals.

NOTE: This is an specialized seminar. If you want to attend this seminar, please contact Tommaso  Flaminio (tommaso@iiia.csic.es).