A quantitative analysis of modal logic

Journal of Symbolic Logic 59 (1):209-252 (1994)
  Copy   BIBTEX

Abstract

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".

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 90,593

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Analytics

Added to PP
2009-01-28

Downloads
38 (#365,484)

6 months
3 (#445,838)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

Citations of this work

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.
Sts: A Structural Theory Of Sets.A. Baltag - 1999 - Logic Journal of the IGPL 7 (4):481-515.

View all 7 citations / Add more citations

References found in this work

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.
Theory of Recursive Functions and Effective Computability.Hartley Rogers - 1971 - Journal of Symbolic Logic 36 (1):141-146.
Normal forms in modal logic.Kit Fine - 1975 - Notre Dame Journal of Formal Logic 16 (2):229-237.
Decidability for branching time.John P. Burgess - 1980 - Studia Logica 39 (2-3):203-218.

View all 12 references / Add more references