Conditional beliefs: From neighbourhood semantics to sequent calculus

Review of Symbolic Logic 11 (4):736-779 (2018)

Authors
Sara Negri
University of Helsinki
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. In this article both the semantics and the proof theory for this logic are studied. First, a natural semantics forCDLis defined in terms of neighbourhood models, a multi-agent generalisation of Lewis’ spheres models, and it is shown that the axiomatization ofCDLis sound and complete with respect to this semantics. Second, it is shown that the neighbourhood semantics is equivalent to the original one defined in terms of plausibility models, by means of a direct correspondence between the two types of models. On the basis of neighbourhood semantics, a labelled sequent calculus forCDLis obtained. The calculus has strong proof-theoretic properties, in particular admissibility of contraction and cut, and it provides a decision procedure for the logic. Furthermore, its semantic completeness is used to obtain a constructive proof of the finite model property of the logic. Finally, it is shown that other doxastic operators can be easily captured within neighbourhood semantics. This fact provides further evidence of the naturalness of neighbourhood semantics for the analysis of epistemic/doxastic notions.
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DOI 10.1017/s1755020318000023
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References found in this work BETA

Counterfactuals.D. Lewis - 1973 - British Journal for the Philosophy of Science 27 (4):403-405.
Two Modellings for Theory Change.Adam Grove - 1988 - Journal of Philosophical Logic 17 (2):157-170.
On Logics of Knowledge and Belief.Robert Stalnaker - 2006 - Philosophical Studies 128 (1):169-199.
Proof Analysis in Modal Logic.Sara Negri - 2005 - Journal of Philosophical Logic 34 (5-6):507-544.

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