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Foreign Affairs and Trade (1994)
| Venue: | in Proceedings of the Fifth Conference on Theoretical Aspects of Reasoning about Knowledge (TARK 5 |
| Citations: | 2 - 2 self |
BibTeX
@INPROCEEDINGS{Heifetz94foreignaffairs,
author = {Aviad Heifetz},
title = {Foreign Affairs and Trade},
booktitle = {in Proceedings of the Fifth Conference on Theoretical Aspects of Reasoning about Knowledge (TARK 5},
year = {1994},
pages = {95--107},
publisher = {Morgan Kaufmann}
}
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Abstract
It is known that a theory in S5-epistemic logic with several agents may have numer-ous 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. I am grateful to Dov Samet for fruitful discussions. 95 It is well established that models for the ordinary propositional calculus are essen-tially unique. A model is a set of states, where each formula in the language is associated with the set of states where it holds, such that conjunction of formulas corresponds to
Keyphrases
foreign affair s5-epistemic logic fruitful discussion infinitary logic formula corresponds s5-axiomatic system dov samet several agent semantics persists model specifies infinite intersection infinite conjunction ordinary propositional calculus strong completeness theorem expressive power numer-ous model
