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Automated Proof Search System for Logic of Correlated Knowledge
American Journal of Mathematical and Computer Modelling
Volume 5, Issue 2, June 2020, Pages: 29-42
Received: Oct. 4, 2019; Accepted: Mar. 2, 2020; Published: Apr. 14, 2020
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Authors
Haroldas Giedra, Institute of Computer Science, Vilnius University, Vilnius, Lithuania
Romas Alonderis, Institute of Data Science and Digital Technologies, Vilnius University, Vilnius, Lithuania
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Abstract
Logic of correlated knowledge is one of the latest development in logical systems, allowing to handle information about quantum systems. Quantum system may consist of one or more elementary particles. Associating agent to each particle, we get multi-agent system, where agents can perform observations and get results. Allowing communication between agents, correlations such as quantum entanglement can be extracted. This can not be done by traditional epistemic logic or logic of distributed knowledge. Our main scientific result is proof search system GS-LCK-PROC for logic of correlated knowledge, which lets to reason about knowledge automatically. The core of the system is the sequent calculus GS-LCK with the properties of soundness, completeness, admissibility of cut and structural rules, and invertibility of all rules. The ideas of semantic internalization are used to get such properties for the calculus. The calculus provides convenient means for backward proof search and decision procedure for logic of correlated knowledge. The procedure generates a finite model for each sequent. As a result we get termination of the proof search and decidability of logic of correlated knowledge.
Keywords
Logic of Correlated Knowledge, Sequent Calculus, Automated Proof System, Decidability, Soundness, Completeness, Admissibility of the Cut Rule
To cite this article
Haroldas Giedra, Romas Alonderis, Automated Proof Search System for Logic of Correlated Knowledge, American Journal of Mathematical and Computer Modelling. Vol. 5, No. 2, 2020, pp. 29-42. doi: 10.11648/j.ajmcm.20200502.11
Copyright
Copyright © 2020 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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