Nested sequents for the logic of conditional belief

Abstract : The logic of conditional belief, called Conditional Doxastic Logic (CDL), was proposed by Board, Baltag and Smets to model revis-able belief and knowledge in a multi-agent setting. We present a proof system for 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 CDL. As a by-product we also obtain a nested sequent calculus for multi-agent modal logic S5i.
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https://hal.archives-ouvertes.fr/hal-02077057
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Submitted on : Friday, March 22, 2019 - 3:56:10 PM
Last modification on : Wednesday, April 3, 2019 - 1:59:36 AM
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Marianna Girlando, Bjoern Lellmann, Nicola Olivetti. Nested sequents for the logic of conditional belief. 2019. ⟨hal-02077057⟩

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