David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Studia Logica 71 (1):57-86 (2002)
In order to capture the concept of common knowledge, various extensions of multi-modal epistemic logics, such as fixed-point ones and infinitary ones, have been proposed. Although we have now a good list of such proposed extensions, the relationships among them are still unclear. The purpose of this paper is to draw a map showing the relationships among them. In the propositional case, these extensions turn out to be all Kripke complete and can be comparable in a meaningful manner. F. Wolter showed that the predicate extension of the Halpern-Moses fixed-point type common knowledge logic is Kripke incomplete. However, if we go further to an infinitary extension, Kripke completeness would be recovered. Thus there is some gap in the predicate case. In drawing the map, we focus on what is happening around the gap in the predicate case. The map enables us to better understand the common knowledge logics as a whole.
|Keywords||Philosophy Logic Mathematical Logic and Foundations Computational Linguistics|
|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
Jan Plaza (2007). Logics of Public Communications. Synthese 158 (2):165 - 179.
Nobu-Yuki Suzuki (1995). Constructing a Continuum of Predicate Extensions of Each Intermediate Propositional Logic. Studia Logica 54 (2):173 - 198.
Nobu-Yuki Suzuki (2003). Halldén-Completeness in Super-Intuitionistic Predicate Logics. Studia Logica 73 (1):113 - 130.
Luc Lismont & Philippe Mongin (2003). Strong Completeness Theorems for Weak Logics of Common Belief. Journal of Philosophical Logic 32 (2):115-137.
Nobu-Yuki Suzuki (1993). Some Results on the Kripke Sheaf Semantics for Super-Intuitionistic Predicate Logics. Studia Logica 52 (1):73 - 94.
Frank Wolter (2000). First Order Common Knowledge Logics. Studia Logica 65 (2):249-271.
Nobu-Yuki Suzuki (1990). Kripke Bundles for Intermediate Predicate Logics and Kripke Frames for Intuitionistic Modal Logics. Studia Logica 49 (3):289 - 306.
Mamoru Kaneko & Takashi Nagashima (1996). Game Logic and its Applications I. Studia Logica 57 (2-3):325 - 354.
Added to index2009-01-28
Total downloads5 ( #255,802 of 1,410,035 )
Recent downloads (6 months)1 ( #177,059 of 1,410,035 )
How can I increase my downloads?