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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
Contributor : Marianna Girlando <>
Submitted on : Friday, March 22, 2019 - 3:56:10 PM
Last modification on : Tuesday, February 9, 2021 - 5:50:03 PM
Long-term archiving on: : Sunday, June 23, 2019 - 3:53:30 PM

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  • HAL Id : hal-02077057, version 1

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Marianna Girlando, Bjoern Lellmann, Nicola Olivetti. Nested sequents for the logic of conditional belief. JELIA - European Conference on Logics in Artificial Intelligence, May 2019, Rende, Italy. ⟨hal-02077057⟩

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