FIRST-ORDER MATHEMATICAL FUZZY LOGIC WITH HEDGES

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In this paper, we consider first-order mathematical fuzzy logic expanded by many hedges. This is based on the fact that, in the real world, many hedges can be used simultaneously, and some hedge modifies truth (or meaning of sentences) more than another hedge. Moreover, each hedge may or may not have a dual one. We expand two axiomatizations for propositional mathematical fuzzy logic with many hedges to the first-order level and prove a number of completeness results for the resulting logics. We also consider logics with many hedges based on -core fuzzy logics.

Technology

David C. Wyld et al. (Eds) : DBDM, CICS, CSIP, AI&FL, SCOM, CSE, CCNET-2016
pp. 85–96, 2016. © CS & IT-CSCP 2016 DOI : 10.5121/csit.2016.60509
FIRST-ORDER MATHEMATICAL FUZZY
LOGIC WITH HEDGES
Van-Hung Le
Faculty of Information Technology,
Hanoi University of Mining and Geology, Vietnam
levanhung@humg.edu.vn
ABSTRACT
In this paper, we consider first-order mathematical fuzzy logic expanded by many hedges. This
is based on the fact that, in the real world, many hedges can be used simultaneously, and some
hedge modifies truth (or meaning of sentences) more than another hedge. Moreover, each hedge
may or may not have a dual one. We expand two axiomatizations for propositional
mathematical fuzzy logic with many hedges to the first-order level and prove a number of
completeness results for the resulting logics. We also consider logics with many hedges based
on -core fuzzy logics.
KEYWORDS
Mathematical Fuzzy Logic, First-Order Logic, Hedge, Strong Completeness, Standard
Completeness
1. INTRODUCTION

Computer Science & Information Technology (CS & IT) 87
2.2. An Axiomatization for Many Hedges

88 Computer Science & Information Technology (CS & IT)
2.3. Mathematical Fuzzy logic with Many Dual Hedges

Computer Science & Information Technology (CS & IT) 89

90 Computer Science & Information Technology (CS & IT)
3. FIRST-ORDER MATHEMATICAL FUZZY LOGIC WITH HEDGES

Computer Science & Information Technology (CS & IT) 91

92 Computer Science & Information Technology (CS & IT)

Computer Science & Information Technology (CS & IT) 93
4. LOGICS WITH HEDGES BASED ON A -CORE FUZZY LOGIC

94 Computer Science & Information Technology (CS & IT)

Computer Science & Information Technology (CS & IT) 95
5. CONCLUSION
ACKNOWLEDGEMENTS
Funding from HUMG under grant number T16-02 is acknowledged.
REFERENCES

96 Computer Science & Information Technology (CS & IT)
AUTHOR
Van-Hung Le received a B.Eng. degree in Information Technology from Hanoi
University of Science and Technology (formerly, Hanoi University of Technology) in
1995, an M.Sc. degree in Information Technology from Vietnam National University,
Hanoi in 2001, and a PhD degree in Computer Science from La Trobe University,
Australia in 2010. He is a lecturer in the Faculty of Information Technology at Hanoi
University of Mining and Geology. His research interests include Fuzzy Logic, Logic
Programming, Soft Computing, and Computational Intelligence.

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Webinar Recording: https://www.panagenda.com/webinars/why-teams-call-analytics-is-critical-to-your-entire-business Nothing is as frustrating and noticeable as being in an important call and being unable to see or hear the other person. Not surprising then, that issues with Teams calls are among the most common problems users call their helpdesk for. Having in depth insight into everything relevant going on at the user’s device, local network, ISP and Microsoft itself during the call is crucial for good Microsoft Teams Call quality support. To ensure a quick and adequate solution and to ensure your users get the most out of their Microsoft 365. But did you know that ‘bad calls’ are also an excellent indicator of other problems arising? Precisely because it is so noticeable!? Like the canary in the mine, bad calls can be early indicators of problems. Problems that might otherwise not have been noticed for a while but can have a big impact on productivity and satisfaction. Join this session by Christoph Adler to learn how true Microsoft Teams call quality analytics helped other organizations troubleshoot bad calls and identify and fix problems that impacted Teams calls or the use of Microsoft365 in general. See what it can do to keep your users happy and productive! In this session we will cover - Why CQD data alone is not enough to troubleshoot call problems - The importance of attributing call problems to the right call participant - What call quality analytics can do to help you quickly find, fix-, and prevent problems - Why having retrospective detailed insights matters - Real life examples of how others have used Microsoft Teams call quality monitoring to problem shoot problems with their ISP, network, device health and more.

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Three things you will take away from the session: • How to run an effective tenant-to-tenant migration • Best practices for before, during, and after migration • Tips for using migration as a springboard to prepare for Copilot in Microsoft 365 Main ideas: Migration Overview: The presentation covers the current reality of cross-tenant migrations, the triggers, phases, best practices, and benefits of a successful tenant migration Considerations: When considering a migration, it is important to consider the migration scope, performance, customization, flexibility, user-friendly interface, automation, monitoring, support, training, scalability, data integrity, data security, cost, and licensing structure Next Wave: The next wave of change includes the launch of Copilot, which requires businesses to be prepared for upcoming changes related to Copilot and the cloud, and to consolidate data and tighten governance ShareGate: ShareGate can help with pre-migration analysis, configurable migration tool, and automated, end-user driven collaborative governance

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FIRST-ORDER MATHEMATICAL FUZZY LOGIC WITH HEDGES

1. David C. Wyld et al. (Eds) : DBDM, CICS, CSIP, AI&FL, SCOM, CSE, CCNET-2016 pp. 85–96, 2016. © CS & IT-CSCP 2016 DOI : 10.5121/csit.2016.60509 FIRST-ORDER MATHEMATICAL FUZZY LOGIC WITH HEDGES Van-Hung Le Faculty of Information Technology, Hanoi University of Mining and Geology, Vietnam levanhung@humg.edu.vn ABSTRACT In this paper, we consider first-order mathematical fuzzy logic expanded by many hedges. This is based on the fact that, in the real world, many hedges can be used simultaneously, and some hedge modifies truth (or meaning of sentences) more than another hedge. Moreover, each hedge may or may not have a dual one. We expand two axiomatizations for propositional mathematical fuzzy logic with many hedges to the first-order level and prove a number of completeness results for the resulting logics. We also consider logics with many hedges based on -core fuzzy logics. KEYWORDS Mathematical Fuzzy Logic, First-Order Logic, Hedge, Strong Completeness, Standard Completeness 1. INTRODUCTION

2. 86 Computer Science & Information Technology (CS & IT) 2. PRELIMINARIES 2.1. Preliminaries on Mathematical Fuzzy Logic

3. Computer Science & Information Technology (CS & IT) 87 2.2. An Axiomatization for Many Hedges

4. 88 Computer Science & Information Technology (CS & IT) 2.3. Mathematical Fuzzy logic with Many Dual Hedges

5. Computer Science & Information Technology (CS & IT) 89

6. 90 Computer Science & Information Technology (CS & IT) 3. FIRST-ORDER MATHEMATICAL FUZZY LOGIC WITH HEDGES

7. Computer Science & Information Technology (CS & IT) 91

8. 92 Computer Science & Information Technology (CS & IT)

9. Computer Science & Information Technology (CS & IT) 93 4. LOGICS WITH HEDGES BASED ON A -CORE FUZZY LOGIC

10. 94 Computer Science & Information Technology (CS & IT)

11. Computer Science & Information Technology (CS & IT) 95 5. CONCLUSION ACKNOWLEDGEMENTS Funding from HUMG under grant number T16-02 is acknowledged. REFERENCES

12. 96 Computer Science & Information Technology (CS & IT) AUTHOR Van-Hung Le received a B.Eng. degree in Information Technology from Hanoi University of Science and Technology (formerly, Hanoi University of Technology) in 1995, an M.Sc. degree in Information Technology from Vietnam National University, Hanoi in 2001, and a PhD degree in Computer Science from La Trobe University, Australia in 2010. He is a lecturer in the Faculty of Information Technology at Hanoi University of Mining and Geology. His research interests include Fuzzy Logic, Logic Programming, Soft Computing, and Computational Intelligence.

FIRST-ORDER MATHEMATICAL FUZZY LOGIC WITH HEDGES

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