A quantitative analysis of modal logic

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)
DOI 10.2307/2275262
 Save to my reading list
Follow the author(s)
My bibliography
Export citation
Find it on Scholar
Edit this record
Mark as duplicate
Revision history
Request removal from index
Download options
Our Archive

Upload a copy of this paper     Check publisher's policy     Papers currently archived: 29,511
Through your library
References found in this work BETA
Semantical Analysis of Modal Logic I. Normal Propositional Calculi.Saul A. Kripke - 1963 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 9 (5‐6):67-96.
Decidability for Branching Time.John P. Burgess - 1980 - Studia Logica 39 (2-3):203-218.
Normal Forms in Modal Logic.Kit Fine - 1975 - Notre Dame Journal of Formal Logic 16 (2):229-237.
In so Many Possible Worlds.Kit Fine - 1972 - Notre Dame Journal of Formal Logic 13 (4):516-520.

Add more references

Citations of this work BETA
Coalgebraic logic.Lawrence S. Moss - 1999 - Annals of Pure and Applied Logic 96 (1-3):277-317.
Iterative and Fixed Point Common Belief.Aviad Heifetz - 1999 - Journal of Philosophical Logic 28 (1):61-79.

Add more citations

Similar books and articles
Added to PP index

Total downloads
11 ( #409,306 of 2,180,720 )

Recent downloads (6 months)
1 ( #301,383 of 2,180,720 )

How can I increase my downloads?

Monthly downloads
My notes
Sign in to use this feature

There  are no threads in this forum
Nothing in this forum yet.

Other forums