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Nested Sequents for the Logic of Conditional Belief

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

Abstract

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 \(\mathsf {S5}_i\).

Keywords

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

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Copyright information

© Springer Nature Switzerland AG 2019

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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