Infinitary epistemic logic
Pages 95 - 107
Abstract
It is known that a theory in S5-epistemic logic with several agents may have numerous models. This is because each such model specifies also what an agent knows about infinite intersections of events, while the expressive power of the logic is limited to finite conjunctions of formulas. We show that this asymmetry between syntax and semantics persists also when infinite conjunctions (up to some given cardinality) are permitted in the language. We develop a strengthened S5-axiomatic system for such infinitary logics, and prove a strong completeness theorem for them. Then we show that in every such logic there is always a theory with more than one model.
References
[1]
Aumann, R. (1976), Agreeing to Disagree, Annals of Statistics 4, pp. 1236--1239.
[2]
Aumann, R. (1989), Notes on Interactive Epistemology, Cowles Foundation for Research in Economics working paper.
[3]
Chellas, B. F. (1980), Modal Logic, an Introduction, Cambridge University Press.
[4]
Fagin, R. (1993), A Quantitative Analysis of Modal Logic, forthcoming in JSL.
[5]
Fagin, R., Geanakoplos, J., Halpern, J. Y. and Vardi, M. Y. (1992), The Expressive Power of the Hierarchical Approach to Modeling Knowledge and Common Knowledge, Proc. of TARK IV, pp. 229--244.
[6]
Fagin, R., Halpern, Y. J. and Vardi, M. Y. (1991), A Model-Theoretic Analysis of Knowledge, Jour. of the ACM 91(2), pp. 382--428.
[7]
Heifetz, A. (1992), Hierarchic Constructions of Incomplete Information Models, preprint, School of Mathematical Sciences, Tel Aviv University.
[8]
Heifetz, A. and Samet, D. (1993), Universal Partition Structures, IIBR working paper 26/93, Tel Aviv University.
[9]
Hughes G. E. and Cresswell, M. J. (1984), A companion to Modal Logic, Methuen, London.
[10]
Karp, C. R. (1964), Languages with Expressions of Infinite Length, North Holland, Amsterdam.
- Infinitary epistemic logic
Recommendations
First-Order Intuitionistic Epistemic Logic
Logic, Rationality, and InteractionAbstractIntuitionistic epistemic logic (IEL), introduced by Artemov and Protopopescu (2016), accepts the co-reflection axiom: “” in terms of Brouwer-Heyting-Kolmogorov interpretation. There are two variants for IEL, one of which has the axiom “”, while ...
Embedding Linear-Time Temporal Logic into Infinitary Logic: Application to Cut-Elimination for Multi-agent Infinitary Epistemic Linear-Time Temporal Logic
Computational Logic in Multi-Agent SystemsLinear-time temporal logic (LTL) is known as one of the most useful logics for verifying concurrent systems, and infinitary logic (IL) is known as an important logic for formalizing common knowledge reasoning. The research fields of both LTL and IL have ...
Comments
Please enable JavaScript to view thecomments powered by Disqus.Information & Contributors
Information
Published In
Publisher
Morgan Kaufmann Publishers Inc.
San Francisco, CA, United States
Publication History
Published: 13 March 1994
Qualifiers
- Article
Acceptance Rates
Overall Acceptance Rate 61 of 177 submissions, 34%
Contributors
Other Metrics
Bibliometrics & Citations
Bibliometrics
Article Metrics
- 0Total Citations
- 122Total Downloads
- Downloads (Last 12 months)33
- Downloads (Last 6 weeks)11
Reflects downloads up to 17 Nov 2024
Other Metrics
Citations
View Options
Login options
Check if you have access through your login credentials or your institution to get full access on this article.
Sign in