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.
| Published in | American Journal of Mathematical and Computer Modelling (Volume 5, Issue 2) |
| DOI | 10.11648/j.ajmcm.20200502.11 |
| Page(s) | 29-42 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
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Copyright © The Author(s), 2024. Published by Science Publishing Group |
Logic of Correlated Knowledge, Sequent Calculus, Automated Proof System, Decidability, Soundness, Completeness, Admissibility of the Cut Rule
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APA Style
Haroldas Giedra, Romas Alonderis. (2020). Automated Proof Search System for Logic of Correlated Knowledge. American Journal of Mathematical and Computer Modelling, 5(2), 29-42. https://doi.org/10.11648/j.ajmcm.20200502.11
ACS Style
Haroldas Giedra; Romas Alonderis. Automated Proof Search System for Logic of Correlated Knowledge. Am. J. Math. Comput. Model. 2020, 5(2), 29-42. doi: 10.11648/j.ajmcm.20200502.11
AMA Style
Haroldas Giedra, Romas Alonderis. Automated Proof Search System for Logic of Correlated Knowledge. Am J Math Comput Model. 2020;5(2):29-42. doi: 10.11648/j.ajmcm.20200502.11
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Download@article{10.11648/j.ajmcm.20200502.11,
author = {Haroldas Giedra and Romas Alonderis},
title = {Automated Proof Search System for Logic of Correlated Knowledge},
journal = {American Journal of Mathematical and Computer Modelling},
volume = {5},
number = {2},
pages = {29-42},
doi = {10.11648/j.ajmcm.20200502.11},
url = {https://doi.org/10.11648/j.ajmcm.20200502.11},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajmcm.20200502.11},
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.},
year = {2020}
}
TY - JOUR T1 - Automated Proof Search System for Logic of Correlated Knowledge AU - Haroldas Giedra AU - Romas Alonderis Y1 - 2020/04/14 PY - 2020 N1 - https://doi.org/10.11648/j.ajmcm.20200502.11 DO - 10.11648/j.ajmcm.20200502.11 T2 - American Journal of Mathematical and Computer Modelling JF - American Journal of Mathematical and Computer Modelling JO - American Journal of Mathematical and Computer Modelling SP - 29 EP - 42 PB - Science Publishing Group SN - 2578-8280 UR - https://doi.org/10.11648/j.ajmcm.20200502.11 AB - 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. VL - 5 IS - 2 ER -
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