The logic of conditional beliefs: neighbourhood semantics and sequent calculus

Abstract : The logic of Conditional Beliefs has been introduced by Board, Baltag and Smets to reason about knowledge and revisable beliefs in a multi-agent setting. It is shown that the semantics of this logic, defined in terms of plausibility models, can be equivalently formulated in terms of neighbourhood models, a multi-agent generalisation of Lewis' spheres models. On the base of this new semantics, a labelled sequent calculus for this logic is developed. The calculus has strong proof-theoretic properties, in particular cut and contraction are admissible and that the calculus provides a direct decision procedure for this logic. Further, its semantic completeness is used to obtain a constructive proof of the finite model property of the logic.