David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Journal of Symbolic Logic 59 (1):209-252 (1994)
We do a quantitative analysis of modal logic. For example, for each Kripke structure M, we study the least ordinal μ such that for each state of M, the beliefs of up to level μ characterize the agents' beliefs (that is, there is only one way to extend these beliefs to higher levels). As another example, we show the equivalence of three conditions, that on the face of it look quite different, for what it means to say that the agents' beliefs have a countable description, or putting it another way, have a "countable amount of information". The first condition says that the beliefs of the agents are those at a state of a countable Kripke structure. The second condition says that the beliefs of the agents can be described in an infinitary language, where conjunctions of arbitrary countable sets of formulas are allowed. The third condition says that countably many levels of belief are sufficient to capture all of the uncertainty of the agents (along with a technical condition). The fact that all of these conditions are equivalent shows the robustness of the concept of the agents' beliefs having a "countable description".
|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
Igor Douven & Alexander Riegler (2009). Extending the Hegselmann–Krause Model III: From Single Beliefs to Complex Belief States. Episteme 6 (2):145-163.
Hans Van Ditmarsch & Willem Labuschagne (2007). My Beliefs About Your Beliefs: A Case Study in Theory of Mind and Epistemic Logic. Synthese 155 (2):191 - 209.
Eric Pacuit (2007). Understanding the Brandenburger-Keisler Paradox. Studia Logica 86 (3):435 - 454.
Slavian Radev (1987). Infinitary Propositional Normal Modal Logic. Studia Logica 46 (4):291 - 309.
Giacomo Bonanno (2005). A Simple Modal Logic for Belief Revision. Synthese 147 (2):193 - 228.
Stuart C. Shapiro & William J. Rapaport (1991). Models and Minds. In Robert E. Cummins & John L. Pollock (eds.), Philosophy and AI. Cambridge: MIT Press. 215--259.
Natasha Alechina & Brian Logan (2010). Belief Ascription Under Bounded Resources. Synthese 173 (2):179 - 197.
John Cantwell (2005). A Formal Model of Multi-Agent Belief-Interaction. Journal of Logic, Language and Information 14 (4):397-422.
John Cantwell (2006). A Formal Model of Multi-Agent Belief-Interaction. Journal of Logic, Language and Information 15 (4):397-422.
Added to index2009-01-28
Total downloads6 ( #213,890 of 1,101,765 )
Recent downloads (6 months)1 ( #306,516 of 1,101,765 )
How can I increase my downloads?