David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
This is indeed a very nice draft that I have read with great pleasure, and that has helped me to better understand the completeness proof for LCC. Modal fixed point logic allows for an illuminating new version (and a further extension) of that proof. But still. My main comment is that I think the perspective on substitutions in the draft paper is flawed. The general drift of the paper is that relativization, (predicate) substitution and product update are general operations on models, and that it is important to check whether given logical languages are closed under these operations. FO logic is closed under relativization, predicate substitution and product constructions (such as those involved in relative interpretation). The minimal modal logic is closed under relativization, which explains the reduction of epistemic logic (withhout common knowledge) + public announcement to epistemic logic simpliciter (as observed in Van Benthem, ). The reduction breaks down as soon as one adds common knowledge. The minimal modal logic is also closed under substitution, which explains the reduction of epistemic logic plus (publicly observable) factual change to epistemic logic simpliciter, via the following reduction axioms (I use !p := φ for the operation of publicly changing the truth value of p to φ): [!p := φ]p ↔ φ [!p := φ]q ↔ q (p and q syntactically different ) [!p := φ]¬ψ ↔ ¬[!p := φ]ψ [!p := φ](ψ1 ∧ ψ2) ↔ [!p := φ]ψ1 ∧ [!p := φ]ψ2 [!p := φ][i]ψ ↔ [i][!p := φ]ψ Unlike the case of relativisation, this can be extended to the case of epistemic logic with common knowledge, by means of: [!p := φ]CGψ ↔ CG[!p := φ]ψ We get the following..
|Keywords||No keywords specified (fix it)|
|Categories||categorize this paper)|
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
No references found.
Citations of this work BETA
No citations found.
Similar books and articles
Johan Van Benthem (2006). Modal Frame Correspondences and Fixed-Points. Studia Logica 83 (1-3):133-155.
Johan van Benthem (2007). Dynamic Logic for Belief Revision. Journal of Applied Non-Classical Logics 17 (2):129-155.
L. Lismont (1994). Common Knowledge: Relating Anti-Founded Situation Semantics to Modal Logic Neighbourhood Semantics. [REVIEW] Journal of Logic, Language and Information 3 (4):285-302.
Johan Van Benthem (2005). Minimal Predicates. Fixed-Points, and Definability. Journal of Symbolic Logic 70 (3):696 - 712.
Johan van Benthem (2004). What One May Come to Know. Analysis 64 (2):95–105.
Added to index2009-01-28
Total downloads6 ( #195,517 of 1,096,588 )
Recent downloads (6 months)1 ( #258,571 of 1,096,588 )
How can I increase my downloads?