Nested Sequents for the Logic of Conditional Belief

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11468)


The logic of conditional belief, called Conditional Doxastic Logic (\(\mathsf {CDL}\)), was proposed by Board, Baltag and Smets to model revisable belief and knowledge in a multi-agent setting. We present a proof system for \(\mathsf {CDL}\) in the form of a nested sequent calculus. To the best of our knowledge, ours is the first internal and standard calculus for this logic. We take as primitive a multi-agent version of the “comparative plausibility operator”, as in Lewis’ counterfactual logic. The calculus is analytic and provides a decision procedure for \(\mathsf {CDL}\). As a by-product we also obtain a nested sequent calculus for multi-agent modal logic \(\mathsf {S5}_i\).


Nested sequent calculus Conditional doxastic logic Belief revision Multi-agent epistemic logic 


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Authors and Affiliations

  1. 1.Aix Marseille University, Université de Toulon, CNRS, LISMarseilleFrance
  2. 2.University of HelsinkiHelsinkiFinland
  3. 3.Technische Universität WienViennaAustria

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