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.
| Original language | American English |
|---|---|
| Title of host publication | Theoretical Aspects of Reasoning About Knowledge |
| Editors | Ronald Fagin |
| Publisher | Elsevier |
| Pages | 95-107 |
| Number of pages | 13 |
| ISBN (Print) | 9781483214535 |
| State | Published - 1994 |
| Event | TARK '94: Proceedings of the 5th conference on Theoretical aspects of reasoning about knowledge - Pacific Grove , California, United States Duration: 13 Mar 1994 → 16 Mar 1994 https://doi.org/10.1016/C2013-0-08309-0 |
Conference
| Conference | TARK '94: Proceedings of the 5th conference on Theoretical aspects of reasoning about knowledge |
|---|---|
| Country/Territory | United States |
| City | California |
| Period | 13/03/94 → 16/03/94 |
| Internet address |