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EVERYONE KNOWS THAT SOMEONE KNOWS: QUANTIFIERS OVER EPISTEMIC AGENTS

Published online by Cambridge University Press:  09 January 2019

PAVEL NAUMOV  and
JIA TAO
PAVEL NAUMOV*
Affiliation:
Department of Mathematical Sciences, Claremont McKenna College
JIA TAO*
Affiliation:
Department of Computer Science, Lafayette College
*
*DEPARTMENT OF MATHEMATICAL SCIENCES CLAREMONT MCKENNA COLLEGE CLAREMONT, CA 91711, USA E-mail: pnaumov@cmc.edu
†DEPARTMENT OF COMPUTER SCIENCE LAFAYETTE COLLEGE EASTON, PA 18042, USA E-mail: taoj@lafayette.edu
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Abstract

Modal logic S5 is commonly viewed as an epistemic logic that captures the most basic properties of knowledge. Kripke proved a completeness theorem for the first-order modal logic S5 with respect to a possible worlds semantics. A multiagent version of the propositional S5 as well as a version of the propositional S5 that describes properties of distributed knowledge in multiagent systems has also been previously studied. This article proposes a version of S5-like epistemic logic of distributed knowledge with quantifiers ranging over the set of agents, and proves its soundness and completeness with respect to a Kripke semantics.

Keywords

03A99epistemic logicquantifiersagentsBarcan formuladistributed knowledge
Type
Research Article
Information
The Review of Symbolic Logic , Volume 12 , Issue 2 , June 2019 , pp. 255 - 270
Copyright
Copyright © Association for Symbolic Logic 2019 

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References

BIBLIOGRAPHY

Artemov, S. (2008). The logic of justification. The Review of Symbolic Logic, 1(4), 477–513.CrossRefGoogle Scholar
Barcan, R. C. (1946). A functional calculus of first order based on strict implication. The Journal of Symbolic Logic, 11(1), 1–16.CrossRefGoogle Scholar
Charrier, T., Ouchet, F., & Schwarzentruber, F. (2014). Big brother logic: Reasoning about agents equipped with surveillance cameras in the plane. Proceedings of the 2014 International Conference on Autonomous Agents and Multi-agent Systems. Richland, SC: International Foundation for Autonomous Agents and Multiagent Systems, pp. 1633–1634.Google Scholar
Cresswell, M. J. (1967). A Henkin completeness for T. Notre Dame Journal of Formal Logic, 8(3), 186–190.CrossRefGoogle Scholar
Fagin, R., Halpern, J. Y., Moses, Y., & Vardi, M. Y. (1995). Reasoning About Knowledge. Cambridge, MA: MIT Press.Google Scholar
Fine, K. (1970). Propositional quantifiers in modal logic. Theoria, 36(3), 336–346.CrossRefGoogle Scholar
Fitting, M. (1999). Barcan both ways. Journal of Applied Non-Classical Logics, 9(2–3), 329–344.CrossRefGoogle Scholar
Fitting, M. (2005). The logic of proofs, semantically. Annals of Pure and Applied Logic, 132(1), 1–25.CrossRefGoogle Scholar
Kripke, S. A. (1959). A completeness theorem in modal logic. The Journal of Symbolic Logic, 24(1), 1–14.CrossRefGoogle Scholar
Lewis, C. I. & Langford, C. H. (1932). Symbolic Logic. New York: The Century Company.Google Scholar
Mendelson, E. (2009). Introduction to Mathematical Logic. Boca Raton, FL: CRC press.Google Scholar
Prior, A. N. (1956). Modality and quantification in S5. The Journal of Symbolic Logic, 21(1), 60–62.CrossRefGoogle Scholar
Sahlqvist, H. (1975). Completeness and correspondence in the first and second order semantics for modal logic. Studies in Logic and the Foundations of Mathematics, 82, 110–143. (Proceedings of the 3rd Scandinavial Logic Symposium, Uppsala, 1973).Google Scholar