Conditional beliefs: From neighbourhood semantics to sequent calculus

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

Sara Negri
University of Helsinki
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.
Keywords No keywords specified (fix it)
Categories (categorize this paper)
DOI 10.1017/s1755020318000023
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

Our Archive

Upload a copy of this paper     Check publisher's policy     Papers currently archived: 43,914
External links

Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library

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.

View all 11 references / Add more references

Citations of this work BETA

Add more citations

Similar books and articles

Reasoning About Collectively Accepted Group Beliefs.Raul Hakli & Sara Negri - 2011 - Journal of Philosophical Logic 40 (4):531-555.
Labeled Sequent Calculus for Justification Logics.Meghdad Ghari - 2017 - Annals of Pure and Applied Logic 168 (1):72-111.
Dual-Context Sequent Calculus and Strict Implication.Kentaro Kikuchi - 2002 - Mathematical Logic Quarterly 48 (1):87-92.
A Sequent Calculus for Urn Logic.Rohan French - 2015 - Journal of Logic, Language and Information 24 (2):131-147.
Cuts, Gluts and Gaps.Vincent Degauquier - 2012 - Logique Et Analyse 55 (218):229-240.
Sequent Calculi And Quasivarieties.Katarzyna Palasinska - 2000 - Reports on Mathematical Logic:107-131.
2-Sequent Calculus: A Proof Theory of Modalities.Andrea Masini - 1992 - Annals of Pure and Applied Logic 58 (3):229-246.


Added to PP index

Total views
13 ( #614,094 of 2,266,272 )

Recent downloads (6 months)
4 ( #353,632 of 2,266,272 )

How can I increase my downloads?


My notes

Sign in to use this feature